1.2.9 Ponchon Savarit

Label h-xy diagram

Points: 1 No answer

Match the labeles correctly to the given diagram!

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Conode

Dew point curve

$$\Delta h_1^{LV}(\vartheta^{sat}_1)$$

$$\Delta h_2^{LV}(\vartheta^{sat}_2)$$

Bubble point curve

Superheated vapor

Vapor-liquid-equilibrium

Subcooled liquid

Enthalpy balance

Points: 1 No answer

The enthalpy balances of the rectification column according to the Ponchon-Savarit method are given below. Match the enthalpies to the schematic diagram!

Note: For this task only, it is assumed that the balance boundaries of the enriching and stripping section match exactly with the first and last separation stage of the column.

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$$h^D$$

$$h^G$$

$$h^{G,Enr}$$

$$\pi^B$$

$$h^{G,Str}$$

$$h^{L,Str}$$

$$h^F$$

$$h^B$$

$$h^{L,Enr}$$

$$\pi^C$$

1.2.9 Labelling Ponchon Savarit rectification

Points: 12 No answer

Please drag the text fields to the correct position on the Ponchon Saverit diagram of the binary mixture of ethanol (1) and water (2) and drop it there. The diagram is given for $$0.1MPa$$. Before you start dragging and dropping recall:

We here assume an adiabatic S&E column. --> Conservation of enthalpy
The abscissa shows the weight fraction $$w_1$$. So the pure compounds are represented on the very right and left sides.
The dashed grey lines are the tie lines, which combine mixtures (phases), which are in thermodynamic equilibrium. If the tie line is vertical, the coexisting phases feature the same composition (-->azeotropic point)
The specific enthalpy of the pure compounds is ZERO, for the reference state of LIQUID, $$0.1MPa$$ and $$0°C$$

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element here

Boiling point curve

$$\pi^B$$ Enthalpy pole point of stripper

Composition of low boiling azeotrope

Range of enricher stage construction

Operational lines stripper

Dew point curve

Specific evaporation enthalpy of pure ethanol

Specific evaporation enthalpy
of pure water

Operational feed line

Operational lines enricher

Range of stripper stage construction

$$\pi^D$$ Enthalpy pole point of enricher

1.2.9 Different reflux ratios Ponchon Savarit

Points: 3 No answer

The figure below shows three potential feed operation lines a, b and c in the Ponchon Saverit diagram. Please assign these operational feed lines to the correct statements. The feed is added with a temperature of $$82°C$$.

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The reflux $$R^L$$ and reboil ratios $$R^G$$ exceed the minimum reflux $$R^L_{min}$$ and minimum reboil ratios $$R^G_{min}$$. As a consequence, the slopes of the operational lines are steeper than the slopes of the tie lines! The stage construction (and also the column) will work!

The smallest possible reflux and reboil ratios, also referred to $$R^L_{min}$$ and $$R^G_{min}$$. The energy demand is minimum in this case, but the number of separation stages is infinite!

-->small operation expenditures (OPEX), but infinite capital expenditures (CAPEX)

The reflux $$R^L$$ and reboil ratios $$R^G$$ go below the minimum reflux $$R^L_{min}$$ and minimum reboil ratios $$R^G_{min}$$. As a consequence, the slopes of the operational lines are flatter than the slopes of the tie lines. The stage construction (and also the column) are not going to work!

1.2.9 min reflux ratio from PS

Points: 10 No answer

This task shows how you can derive the minimum external reflux $$R^L_{min}$$ and reboil $$R^G_{min}$$ ratios from a Ponchon Savarit diagram, if you know some boundary conditions about the rectification task. The figure below shows the Ponchon Savarit diagram for the binary mixture of ethanol (1) and water (2) for a pressure of $$0.1MPa$$.

This is what we know about the rectificatin task:

The feed mass flow rate is $$108kg/h=0.03kg/s$$
The feed weight composition is $$w_1=0.5$$
The feed temperature is $$84.5°C$$
The bottom product weight composition is $$w^B_1=0.05$$ and the distillate weight composition is $$w^D_1=0.9$$

You know from the previous OPAL tasks that the minimum external reflux $$R^L_{min}$$ and reboil $$R^G_{min}$$ ratios are expressed by the connection line between the two pole points (feed operation line), which has the slope of the tie line crossing the feed point. The feed temperature is $$84.5°C$$ and thus the feed operation line (yellow) hast to be the extension of the respective tie line (grey dashed). As we also know the weight composition of the bottom product and the distillate, the pole pints $$\pi^B_{min}$$ and $$\pi^D_{min}$$ are defined. You can then see the respective enthalpy pole points in the figure.

If the feed was added with a caloric state $$q^F=1$$, its specific enthalpy would have been $$h^F({q^F=1})=$$ Close tooltip $$kcal/kg$$.
If the feed was added with a caloric state $$q^F=0$$, its specific enthalpy would have been $$h^F({q^F=0})=$$ Close tooltip $$kcal/kg$$.
In this task the feed is added with a caloric state of $$q^F=$$ Close tooltip (precision 1 digit after decimal point; read from figure), which results in a specific enthalpy of $$h^F=$$ Close tooltip $$kcal/kg$$ (precision 0 digit after decimal point; read from figure).

The mass flow rate of the bottom product is Close tooltip $$kg/s$$ (precision 4 digits after decimal point).
The mass flow rate of the distillate is Close tooltip $$kg/s$$ (precision 4 digits after decimal point).

For the computation of the following two questions, you have to use the equation for the computation of the enthalpy pole points. The specific enthalpy of the saturated distillate and the specific evaporation enthalpy of the distillate can be read from the Ponchon Savarit diagram. The same is true for the bottom product.

The minimum cooling power of the condenser is $$Q ̇^C_{min}=$$ Close tooltip $$kcal/s$$ (as positive value with 4 digits precision after the decimal point).
The minimum heating power of the reboiler is $$Q ̇^B_{min}=$$ Close tooltip $$kcal/s$$ (as positive value with 4 digits precision after the decimal point).

Meanwhile you know the

heating and cooling utilities,
the mass flow rates of the distillate and the bottom product
the specific enthalpies of the saturated distillate and the saturated bottom product
and the specific evaporation enthalpies of the bottom product and the distillate.

Summarizing, you have all information available, which is required for the computation of the minimum external reflux $$R^L_{min}$$ and reboil $$R^G_{min}$$ ratios.
The minimum external reflux ratio $$R^L_{min}=$$ Close tooltip (precision 4 digits after decimal point).
The minimum external reboil ratio $$R^G_{min}=$$ Close tooltip (precision 4 digits after decimal point).

1.2.9 Ponchon Savarit correct or wrong

Points: 4 No answer

Please assign the text statements to the respective stage constructions in the Ponchon Savarit diagram.

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Reboil $$R^G$$ & reflux $$R^L$$ ratios are smaller than the minimum reboil $$R^G_{min}$$ and minimum reflux ratio $$R^L_{min}$$, respectively.

the slope of some operation lines become smaller than the slope of the tie lines in the respective region. Compare for example the slopes of the tie lines in the region of the feed operation line (the one connecting the two pole points). The slope of the feed operation curve is "flatter" than the slope of the tie lines. As a consequence the stage construction cannot be constructed from the left to the right pole point. It is identical to too small reflux and reboil ratios in the McCabe Thiele diagram.

Wrong stage construction in enriching section:

the equilibria lines (grey arrows) are not interpolated between the neighbouring tie lines. So the grey arrows intersect the tie lines. This is prohibited!

Wrong stage construction in stripping section:

the equilibria lines (grey arrows) are not interpolated between the neighbouring tie lines. So the grey arrows intersect the tie lines. This is prohibited!

Correct stage construction in enricher and stripping section:

all operation lines intersect in the pole points
there is one common feed operation line, which combines both pole points
the equilibria lines (grey arrows) are interpolations between the tie lines. They MUST NOT cross the tie lines!

Calculate feed state (1)

Points: 2 No answer

A feed solution of methanol and water with the molar fraction $$z^F = 0.25$$ and $$\vartheta$$ = 20 °C at $$p$$ = 1.013 bar should be added to the rectification column as boiling liquid.

Determine the molar heat $$q$$ that must be transferred to the feed solution as well as the resulting temperature $$\vartheta^F$$ of the feed using the data given!

The molar heat capacities of the pure substances are assumed to be independent of temperature:

- Methanol: $$c_{p,1}^L$$ = 85.01 J/(mol K)

- Water: $$c_{p,2}^L$$ =75.47 J/(mol K)

All enthalpies of the mixture are assumed to be linear combinations of the enthalpies of the pure substances, whereby the heat of mixing is neglected.

$$q$$	=	Close tooltip	kJ/mol
$$\vartheta^F$$	=	Close tooltip	°C

Calculation of enthalpy

Points: 1 No answer

Match the equations for calculating enthalpy of a pure substance to the corresponding states!

The reference state is defined as liquid at 0 °C and the specific heat capacities are assumed to be temperature independent.

$$\vartheta$$ - temperature in °C

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subcooled liquid

boiling liquid

saturated vapor

superheated vapor

$$h(\vartheta) = c_p^L \cdot \vartheta$$

$$h(\vartheta) = c_p^L \cdot \vartheta^{sat} +\Delta h^{LV}(\vartheta^{sat}) + c_p^V \cdot (\vartheta - \vartheta^{sat})$$

$$h(\vartheta=\vartheta^{sat}) = c_p^V \cdot \vartheta - \Delta h^{LV}(\vartheta)$$

$$h(\vartheta=\vartheta^{sat}) = c_p^L \cdot \vartheta$$

$$h(\vartheta) = c_p^L \cdot \vartheta^{sat} +\Delta h^{LV}(\vartheta^{sat}) + c_p^V \cdot \vartheta$$

$$h(\vartheta=\vartheta^{sat}) = c_p^V \cdot \vartheta + \Delta h^{LV}(\vartheta)$$

$$h(\vartheta) = c_p^V \cdot \vartheta$$

$$h(\vartheta = \vartheta^{sat}) = c_p^L \cdot \vartheta +\Delta h^{LV}(\vartheta)$$

Reflux ratio (1)

Points: 1 No answer

The figure shows schematic h-xy diagrams representing three different reflux ratios $$R^L$$. Match the terms to the diagrams!

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$$R^L = R^L_{min}$$

$$R^L < R^L_{min}$$

$$R^L > R^L_{min}$$

Reflux ratio (2)

Points: 1 No answer

The (minimum) reflux ratio $$R^L_{(min)}$$ can be determined by balancing the condensor (see figure).

Complete the equations with the given terms!

$$\dot D$$

$$h^G$$

$$\pi^D$$

$$\dot Q_C$$

$$(1+R^L)$$

$$h^D$$

$$R^L \dot D$$

Reflux ratio (3)

Points: 6 No answer

Conclusion:

For the minimum reflux ratio, the mixing line (overall material balance) goes along the conode through the feed point.

In this case the resulting specific cooling utility of the condenser is and the specific heating utility of the reboiler is .

The number of separation stages is .

This means: The closer the reflux ratio is to the minimum value, the the investment costs and the the operating costs.