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Identifying and Monitoring Leakage in a CSTR System

## Problem 1

Problem 1: A team of consultant engineers needs to monitor and identify potential leakages in a prototype CSTR (continuously stirred tank reactor) system. After a few weeks of operation, leakage (FluidX) was detected through one of the valve manifolds. From preliminary tests, Fluid X can be eithermethane, ethane, propane, ethylene or cyclopentane. In order to fifix the problem, the team mustfifirst identify the flfluid that leaked from CSTR system. A testing-cell was designed to investigatethe PVT behaviour of flfluids under a wide range of pressure (P660 bar) and temperature (T6800K). Fluid X was injected into the cell with fifinal molar volume of 1.0 litre mol

1

. The cell was heatedfrom 400 to 600 K and the pressure change is shown in Table 1.

T (K) 400 420 440 460 480 500 520 540 560 580 600

P (bar) 30.7 33.1 35.3 37.3 38.1 40.0 41.9 44.5 45.3 46.4 50.0

Table 1: Experimental P P T data for Fluid X.

Task 1 [Hand calculation] Assuming that Fluid X can be either methane or cyclopentane, calculate the compressibility factor (Z) of both flfluids at 480 K using the following equations of state:

i. van der Waals;

ii. Soave-Redlich-Kwong.

Compare the values obtained at this temperature with the experimental compressibility factors of Fluid X,

ε (%) =

Z calc × Z exp

Zexp × 100

Task 2 [Matlab code] Write a Matlab code to calculate compressibility factors of flfluids for 4006T6600 K (with temperature intervals of ?T = 20 K) using the following equations of state:

i. van der Waals;

ii. Redlich-Kwong;

iii. Soave-Redlich-Kwong;

iv. Peng-Robinson.

With this code:

i. Plot P P T curves for Fluid X, methane, ethane, propane, ethylene or cyclopentane (1 plotfor each EOS);

Dr Jeff Gomes 1EX3029 – Chemical Thermodynamics EOS and VLE assignment

Molecular Weight ω Tc Pc Zc Vc

g mol

1

(K) (bar) cm

3

mol

Methane 16.043 0.012 190.6 45.99 0.286 98.6

Ethane 30.070 0.100 305.3 48.72 0.279 145.5

Propane 44.097 0.152 369.8 42.48 0.276 200.0

Ethylene 70.134 0.087 282.3 50.40 0.281 131.0

Cyclopentane 16.043 0.196 511.8 45.02 0.273 258.0

Table 2: Thermophysical properties of hydrocarbons.

ii. From the simulation data, you should be able to (numerically) identify Fluid X and the best EOS to predict its PVT behaviour. Calculate averaged compressibility factor of Fluid X from experimental data and identifified flfluid (using the best EOS).

Thermophysical properties of the flfluids may be found in Table 2.

Problem 2: For gaseous toluene at 285?

C:

Task 1 [Hand calculation] Calculate the compressibility factor (Z) and molar volume in m3

mol

at reduced pressures of 1.0×10 3

and 0.95 using the Soave-Redlich-Kwong EOS;

Task 2 [Matlab code] Plot a Pr-Z diagram for reduced pressures (Pr)ranging from 10

5

to 1 ? with ?Pr = 10

2

using Soave-Redlich-Kwong and Peng-Robinson equations of state;

Task 3 [Hand calculation] 17 m

3

mol

1

of gaseous toluene at 19

?

C is compressed from 1 bar to 2.5 bar in a pressure vessel. In order to keep the temperature of flfluid constant, heat needs to be removed from the system. Calculate the heat transferred during this process. Assume that toluene behaves as a Redlich-Kwong flfluid.

Given Tc = 592 K, Pc = 41.3 bar, ω = 0.266 and Cp = 1.72 kJ (kg K) 1.

Problem 3: A mixture containing n-hexane (1), n-heptane (2), n-octane (3), methylcyclohexane (4) and toluene(5) is transported into a flflash vessel where the pressure is reduced to 7.5 bar. The liquid fractionresulting from this flflash vessel is sent to a second flflash vessel where the pressure is further reducedto 2 bar.Dr Jeff Gomes 2EX3029 – Chemical Thermodynamics EOS and VLE assignment