Convincing Features
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Date
1. ANSWER ALL QUESTIONS GIVEN
2. PART 1 SUBMIT ON WEEK 7TH 20 NOVEMBER 2025
3. MUST BE HANDWRITTEN AND IN PDF FORM
4. SUBMISSION WILL THROUGH VLE AND CLOSE ON 4 PM
20TH NOVEMBER 2025
5. STATE ALL REFRENCES USED
In an extraction vessel (Figure A1) an unbuffered wastewater flow FA (the substrate) polluted with aniline with concentration xA,in, is extracted by means of benzene with flow FB (the solvent). The effective distribution coefficient depends on the temperature. Steam with flow Fsteam is added to raise the temperature to a required value of 50 °C. The vessel is will mixed by a stirrer with constant speed. Subsequently, in a phase separator the benzene (the extract) is separated from the water phase (the raffinate). In the separator the two levels can be measured. The fraction aniline in the wastewater should be decreased to xA and increased in the benzene to xB.
Fig. A1. Extraction process consisting of vessel and separator. y = weight fraction water, xA = fraction aniline (ppm) in water, xB = fraction aniline (ppm) in benzene.
Suppose the goal of the process is to produce a wastewater flow which meets the requirement.
a. Q: Design the diagram model for the goal mentioned. Indicate in the diagram: the manipulated variables, the external disturbances and the variables of the process, which should be controlled.
b. Q: Sketch the process and add an initial control scheme consisting of single feedback control loops in agreement with the goal.
c. Q: Indicate in which way a single feed-forward control loop could be used useful. Mention a disadvantage of this control
Process model
The following assumptions can be made for the dynamic model of the extraction process.
a. the fresh (regenerated) benzene contains no aniline
b. the distribution coefficient depends only on the temperature and is independent of the concentration, according the relationship:
α = Aαe-Eα RT ( Eq 1)
c. no extraction occurs in the separator
d. water and benzene are ideal mixed in the extraction vessel
e. the liquid phases are at equilibrium
f. the steam enters at boiling point, hence the cooling down of the steam to the condensation point can be ignored
g. control of the contents of the extraction vessel is based on a pressure difference measurement manipulating the outflow of the extraction vessel, it can therefore be assumed that at ideal control, the total mass is constant.
h. control of the contents of the extraction vessel is ideal and can be considered as a part of the system
i. in the operation area, the density and the specific heat of water and benzene are nor a function of the temperature, neither a function of the aniline concentration. However, the density and the specific heat of the water-benzene mixture depends on the water-benzene ratio (see ρ and cP values).
j. the heat capacities of the walls and mixer can be neglected.
k. the energy added by the stirrer can be neglected
l. the heat loss to the environment can be neglected
Design the behavioral model, which is consistent with the environmental model, for the extraction vessel including the level controller (excluding the separator). ).
The inputs of the system are: FA, TA,in, xA, FB,in, TB,in Fsteam Tsteam and Msetpoint. The outputs are: the water fraction y, which can be expressed as a weight fraction and may be defined as the ratio of mass of water to the total mass, the aniline concentration in the water xA and the temperature T. Please answer the following questions
a. Q: Identify the state variables and determine the state equations. Indicate clearly where which assumption is used.
b. Q: Transfer the state equations in such a way that the left-hand site contains only a derivative of one variable. Check whether the steady state component balance agrees with a one-stage extraction.
c Q: When you define an equation, describe clearly which equation it concerns (mass, component balance…). Indicate clearly where which assumption is used and indicate when additional assumptions were necessary
d. Q: Give the additional algebraic equations and additional assumptions, if required. Indicate clearly where which assumption is used and indicate whether additional assumptions are necessary
e. Q: Design the behavioral model for the extractor, which is consistent with the environmental model and ensure that one function produces one variable. Indicate clearly which equations are used in the diagram e. Q: Check the number of degrees of freedom.When you suggest an equation, indicate clearly which equation you mean by giving it a name
f. Q: Calculate the benzene flow and steam flow for the steady-state conditions, using the following data:
| distribution coefficient: | Aα | 37.2 kg/kg |
| activation energy | Eα | 2350 J/mol |
| gas constant | R | 8.31 J/mol.K |
| waste-water flow | F A,in | 100 kg/min |
| wastewater temperature | TA,in | 25 °C |
| aniline in wastewater flow | xA,in | 300 ppm |
| benzene flow | FB,in | ? kg/min |
| benzene flow temperature | TB,in | 25° C |
| steam flow | Fsteam,in | ? kg/min |
| steam temperature | Tsteam in | 100 °C |
| required vessel temperature | Tvessel | 50 °C |
| required analine in water out | xA,uit | 10 ppm |
| heat capacity water | cP,A | 4.2 kJ/kg.K |
| heat capacity benzene | cP,B | 1.8 kJ/kg.K |
| heat of evaporation water | ΔHsteam | 2.2 MJ/kg |
| water volume extraction | Mvesse | 600 kg |
| vessel volume separator | Mseparator | 3000 (1/3 w |
The assignment concerns the extractor of assignments on section 1 and 2. Only the extraction vessel is considered and some simplifications are made.
A wastewater flow FA (the substrate) polluted with aniline xA,in is extracted by means of benzene with flow FB (the solvent). The effective distribution coefficient depends on the temperature. Steam with flow Fsteam is added to raise the temperature. The vessel is well mixed by a stirrer with constant speed. The fraction aniline in the wastewater is reduced to xA.
Assume that the process can be described by the following equations: Component balance of aniline:
| (𝑀 + 𝛼𝑀 ) = = 𝐹 𝑥𝑀, − (𝐹 + 𝛼𝐹 + 𝐹
16) Under the assumption that: • the specific heat of component A and B are equal • the steam enters at the condensation point • TB < T, TA < T, Tsteam > T the energy balance can be written as: 𝑑𝑇 𝐶 (𝑀 + 𝛼𝑀 ) 𝑑 |
)𝑥 | (Equation No |
| = 𝐶 𝐹 (𝑇 − 𝑇) + 𝐶 𝐹 + 𝛼𝐹 (𝑇 | − 𝑇) | |
| + 𝐶 𝐹 (𝑇 − 𝑇)+ ∇𝐻 𝐹 | ||
The distribution coefficient can be given by eqn. (Eq 1).
The steady-state distribution of MA and MB can be given by
𝑀 𝐹 + 𝐹
=
𝑀 𝐹
Define the residence time
𝑀 𝑀
= = 𝜏
𝐹 + 𝐹 𝐹
| Input | FA, FB, Fsteam
TA, TB, Tsteam xA,in |
incoming flows A, B, steam temperatures of incoming flows, pollution fraction in FA | Kg/s
°C ppm |
| Output | T xA | temperature extraction vessel, pollution fraction in A in vessel | °C
Kg/kg |
| Internal variables | α
MA, MB |
distribution coefficient mass of A and B in vessel | Kg/kg kg |
| Constants: | ΔHsteam | specific heat heat of evaporation | J/kg °C J/kg |
a. Q: Linearize the equations mentioned above and transfer these relationships to deviation variables. Indicate deviation variables with the symbol . Terms of the order equal to or higher than δ 2 may be ignored.
b. Q: Determine the transfer function between xA and FB.
Hint: use positive time constants to simplify the equations and calculations. Define clearly the meaning of the constants in the final result
c. Q: Is the system determined under b. stable? Can it oscillate? Under which conditions can an inverse response occur? Is this situation realistic? Try to explain how the system works physically.
d. Q: Determine the transfer function between xA and Fsteam.
e. Q: Suppose that the influence of a change in FB on a change in T is small and can be ignored. In addition, assume that the impact of a change in Fsteam on a change in xA is small compared to the impact of a change in T on a change in xA. What is then the essential difference between the dynamics of xA caused by changes in FB and in Fsteam? Which flow is more suitable for control of xA? transfer functions can then be written as:
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