The theoretical number of stages of an immiscible liquid

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The main purpose of this experiment is to calculate the theoretical number of stages of an immiscible liquid-liquid extraction system using McCabe-Thiele diagram. Furthermore, to evaluate overall mass transfer coefficient and to find the height of the operating unit.

The procedure followed in the calculation of theoretical number of stages was based on McCabe-Thiele diagram, merely by plotting the equilibrium curve using the mass ratio data (Y,X) and at least one operating line.

The theoretical number of stages were determined and it was found from McCabe-Thiele diagram that the transfer unit have 1.2 equilibrium stages and a height equal to 2.6 m with percentage error equal to 54.6%. Moreover, the experimental value of mass flow rate ratio (Fd/Fs) was calculated then it was compared to the theoretical value to give percentage error of 30.85 %.

Finally, it was concluded that there are different sources of errors including the adjustment of the flow rate. In addition, it was found that as speed of the rotation of the spinning band increased, a better extraction process would be obtained.

Separation process is classified to be one of the most significant processes in any chemical industry to present and purify chemicals compound before stepping inside any chemical reactor and after it. There are several methods used to separate chemical compounds including continuous distillation column, adsorption, stripping and extraction. To remove one or more solutes from a liquid, immiscible liquid-liquid extraction will be the suitable method by transferring the solutes into another liquid phase.
Here are equations that were used in the calculation of this experiment:
X=x/(1-x) Where X = mass ratio solute in diluent (kg A / kg D). (1)
Y=y/(1-y) Where Y = mass ratio solute in solvent (kg A / kg s) . (2)
∆[y]_ln=((y_1^*-y_1 )-(y_(N+1)^*-y_(N+1) ))/(ln⁡((y_1^*-y_1)/(y_(N+1)^*-y_(N+1) ))) (3)
Where y* = extract mass fraction on solute at equilibrium.
K_ca=(W_T (y_1-y_(N+1)))/(∆[y]_ln .V) Where Kca¬ = overall mass transfer (4)
Coefficient (1/s), V = volume of separation column (m3), WT = flow rate of the light phase (m3/s).
H’=W_T/(K_ca .s) Where H’ = height of the unit (m). (5)
H_th=H^’ x N Where N: Number of stages (6)

Table 1: Equilibrium Data for water, Isopropanol and Toluene System and their mass rations.
x y X Y
0.0463 0.0058 0.0485 0.0058
0.0656 0.0092 0.0702 0.0093
0.1013 0.0149 0.1127 0.0151
0.1262 0.0226 0.1444 0.0231
0.1572 0.0356 0.1865 0.0369
0.1872 0.0516 0.2303 0.0544
0.2259 0.0959 0.2918 0.1061
0.2612 0.1538 0.3535 0.1818
0.2955 0.2131 0.4194 0.2708
0.3224 0.2964 0.4758 0.4213

Table 2: Gas Chromatography Analysis of the Feed, Heavy and Light with their mass fractions.
GC analysis Area Ratio Mass Ratio Mass Fraction
Feed (Xo) 0.2523 0.4383 0.3047
Heavy (XN) 0.1235 0.2146 0.1767
Light (Y1) 0.0724 0.0659 0.0618
(YN+1) 0 0 0

Table 3: Comparing experimental ratio (FD/FS) exp to theoretical ratio (FD/FS) Th.
(FD/FS)th 0.295
(FD/FS)exp 0.39
Error% 30.85

Table 4 : Main result Obtained From McCabe-Thiele Diagram and Calculated From experiment.
# of stages (N) 1.2
Y1* 0.3200
y1* 0.2424
Yn+1* 0.0700
yn+1* 0.0654
Δ[y]ln 0.1134
V (m3) 0.0001130
WT (m3/s) 0.00000007600
Kca (eq9) (s^-1) 0.000366
S (m2) 0.0001
H’ (m) 2.2
HTh (m) 2.6
H (m) 1.2
Error % 54.6

Figure 1: McCabe-Thiele Diagram for Dilute Extraction
Discussion of Result:
For separation by extraction, we cannot use the mass fraction like in normal distillation column because the solution is too dilatant however, instead of that we use mass ratio. The mass fraction for the equilibrium data were converted to mass ratio as shown in table (1).

Using the GC analysis with the area ratio %, the mass ratio in the feed(X0), heavy phase (XN) and light phase (Y1) were evaluated then were converted to mass fraction as shown in table (2).

As shown in figure (1), equilibrium data were plotted against operating line then both of the number of theoretical stages and the slope of the operating line (Fd/Fs) were obtained and they were equal to 2.1 stages and 0.295 respectively.

As shown in table (3), the experimental value of mass flow rate ratio (Fd/Fs) was compared to the theoretical value to give percentage error of 30.85 %.

As shown in table (4), the overall mass transfer coefficient was equal to 0.000366 s-1 and the actual height of the unit was evaluated to be 2.6 m with an error equal to 54.6%.

It can be noticed from the experiment that the effect the speed of the spinning band is to enhance the overall mass transfer coefficient and as result a better separation.

In conclusion, quite large errors were estimated regarding both the height of the column (54.6%) and the experimental ratio (Fd/Fs) (30.85 %). The actual height of the unit column is 1.9 m, while the theoretical height of the unit was 2.6 m. In addition, the overall mass transfer coefficient was determined to be 0.000366 s-1 and the number of theoretical stages were 1.2 stages.
However, there were different sources of the errors that were obviously reflected on the results. First, the feed was nearly improperly prepared, which could be seen in the GC analysis. Moreover, it was challenging to adjust the flow rates of the two phases at low rates. Additionally, the most key source of error was because the system could not reach punctually the steady state condition.

Appendices :
A1. Raw Data.
A2. Gas Chromatography Analysis
A3. Sample of Calculations.


Sample Solution