(B) TO VERIFY THE EQUATION (C) TO OBSERVE THE ONSET OF FLUIDIZATION AND DIFFERENTIATE BETWEEN THE CHARACTERISTICS OF A FIXED AND FLUIDIZED BED. (D) TO COMPARE THE PREDICTED ONSET OF FLUIDIZATION WITH THE MEASURED HEAD LOSS.
DATE: 20 TH OF MAY 2021
NAME: NWAFOR CHISOM
MATRICULATION NO: ENG
SERIAL NO: 114
GROUP: B
EXPERIMENT CODE: 03
LEVEL: 300
INSTRUCTOR: MR MOSES OGHENOVO.
Contents . Page no
Theory. Description of Apparatus.
The experiment was carried out to observe characteristics of air flowing vertically upwards through a bed of granular material. To carry out this experiment we had our fixed and fluidized bed experimental set up which consist of the water and air circuit, but the air circuit was the one used to carry out this experiment.
The equipment was turned on and the air compressor pumps air at the air test column through a flow valve connected to a flow meter, the valve was adjusted to cause an increment of 1L/min at each flow rate the pressure drop determined by taking readings from the differential water manometer and also the bed length was noted , this was repeated until we got to 7L/min when the bed start to increase in length hence the bed state changed to fluidized.
Since we have already gotten or experimental pressure drop the theoretical values were gotten from using the relevant formulae for fixed and the fluidized bed, the experimental values and the theoretical values were not the same due to human errors but it was close which goes ahead to prove that the Erguns’ equation is valid.
The flow of a fluid, either liquid or gas, through a static packed bed of particles is a situation encountered both in nature and industry. Natural occurrences include the movement of ground water, the movement of crude petroleum or the movement of natural gas through process media. Industrial occurrences include operations of backwashing filters, ion exchange processes, extraction of soluble components from raw material and certain type of chemical reactors.
The theory for this experiment is covered in Chapter 7 of McCabe, Smith, and Harriott (M,S&H). The following material is a condensation of that chapter as it relates to the experiment at hand. As an aid to you, some specific equations in M,S,&H are referred to. There are three areas of interest to us: (1) Relationship between the pressure drop and the flow rate; (2) Minimum fluidization velocity, and; (3) Behavior of the expanded bed.
(1) Relationship between pressure drop and flow rate The flow of a fluid, either liquid or gas, through a static packed bed can be described in a quantitative manner by defining a bed friction factor, fp, and a particle Reynolds number, NRe,p, as follows:
Note that this equation cannot be derived directly by extrapolating the case of flow through a circular conduit since friction factor defined in both cases is different (see McCabe and Smith 4th edition, pg. 137)
Where ∆P = pressure drop across the bed L = bed depth or length gc = conversion constant (= unity if SI units are used) Dp = particle diameter ρ = fluid density ε = bed porosity or void fraction Vo = superficial fluid velocity μ = fluid viscosity φs = sphericity
The friction factor and the Reynolds number are dimensionless. Some typical sphericity factors are given in McCabe, Smith and Harriott (p. 928, Table 28).
For laminar flow, where only viscous drag forces come into play, NRe,p < ( ), experimental data may be correlated by means of the Kozeny-Carman equation:
Note: According to Yates ("Fundamentals of Fluidized-bed Chemical Processes," by J. G. Yates, Published by Butterworths, 1983, p. 7-8) the factor of 150 was originally given by Carman as 180 for the case of laminar flow. Ergun later suggested a better value was 150 when the particles are greater than about 150 μm in diameter.
For highly turbulent flow where inertial forces predominate, (NRe,p >1000 ) ), experimental results may instead be correlated in terms of the Blake-Plummer equation:
While both equations (3) and (4) have a sound theoretical basis, Ergun empirically found that the friction factor could be described for all values of the Reynolds number by simply adding the righthand sides of equations (3) and (4). Thus:
+1. (2) Minimum fluidization velocity At a sufficiently high flow rate, the total drag force on the solid particles constituting the bed becomes equal to the net gravitational force and the bed becomes fluidized. For this situation a force balance yields:
(−∆p)A=LA (1−εM )(ρp −ρ )g/gc =M (ρp −ρ)g/ (gcρp ) (6) where εM = void fraction at the minimum fluidization velocity A = cross-sectional area of the bed ρp = particle density g = gravitational constant M = total mass of packing. This is Eq. 7, 7 MS&H. The superficial fluid velocity at which the fluidization of the bed commences is called the incipient or minimum fluidization
0<NRe,p <1 n=4,p −0 (12) 1<NRe,p <500 n=4,p −0 (13)
NRe,p >500 n=2 (14) Because the terminal velocity, ut, is a constant for a given particle, it can be seen that Equation (10) above is essentially the same as the empirical equation in the text; namely Eq. (7) MS&H.
The void fraction of the expanded bed, ε, is related to that at incipient fluidization by the following equation:
(7-58 MS&H) where LM and εM are the bed height and void fraction at incipient fluidization, and L is the measured height of the expanded bed. Therefore, since LM and εM are known, ε can be calculated from the measured height, L, of the expanded bed.
In Equations (11)-(14) the Reynolds number is based on the particle diameter, Dp, and the terminal velocity, ut. Therefore it is necessary to know the terminal velocity. By means of a force balance it be shown that the terminal velocity for spherical particles is:
(15, &.37 MS&H) where CD denotes the drag coefficient. A graph of CD versus NRe,p is shown in the text (Figure 7, p. 158). To find CD, you need to know ut so that NRe,p can be calculated. There are two ways of doing this: i) One could do this by trial-and-error. Thus, you could guess ut, calculate NRe,p, look up CD on the graph, and put the resulting value in Eq. (15). If the calculated value of ut did not match the guess (it surely wouldn't on the first try!), you would guess again. ii) We can also do this without trial-and-error. For this square both sides of Eq. (15) and utilize the definition of NRe,p (Eq. (2)) to obtain:
All parameters on the right are known. This suggests that a plot of CDNRe,p 2 versus NRe,p can be constructed and used to avoid the trial-and-error procedure.
The plot is prepared in the following way. Pick a series of point coordinates off the plot shown above. Some examples for spheres are:
Table 1
NRe,p CD CD NRe,p 0 22000 22 0 2200 22 0 220 22 1 0 480
Pick off a dozen similar pairs. Then plot CDNRe,p as the ordinate against corresponding NRe,p as the abscissa. For each bed, calculate CDNRe,p 2 from Eq. (16). From your plot read the corresponding NRe,p. Then use Eq. (2) to calculate ut
When water is passed at very low velocity up through a bed of solid particles, the particles do not move, and the pressure drop is given by the Erguns equation;
Where ΔP = Pressure drop (Nm)
L= height of bed Vsm= average superficial fluid velocity μw= viscosity of water (Nsm-2)
ρw = density of water (kgm-3) DP = size of particles (m)
Фs = particle sphericity ε = bed voidage
If the fluid velocity is steadily increased, the pressure drop and the drag on individual particles increase, and eventually the particles start to move and become suspended in the fluid. The term fluidization and fluidized bed are used to describe the condition of fully suspended particles, since the suspension behaves as a dense
RESULTS
Bed height (mm)
Flow Rate (L/min)
P 1 (mmH 2 O) P 2 (mmH 2 O) Pressure drop in bed ΔP(mmH 2 O)
Bed state
310 0 245 245 0 fixed 310 2 212 278 66 fixed 310 3 196 293 97 fixed 310 4 180 310 130 fixed 310 5 160 329 169 fixed 310 6 140 350 210 fixed 312 7 120 370 250 fluidized 314 8 105 384 279 fluidized 318 9 90 397 307 Fluidized 324 10 88 400 312 Fluidized 333 11 85 403 318 Fluidized 340 12 82 406 324 Fluidized 345 13 80 408 328 Fluidized 350 14 79 409 330 Fluidized 358 15 78 411 333 Fluidized 365 16 75 412 337 Fluidized 373 17 71 415 344 Fluidized 375 18 70 417 347 Fluidized 383 19 69 418 349 Fluidized 398 20 68 419 351 fluidized
Table 2