Risposte teoria prima parte Separation unit operations

Part one: Continuous distillation process

1) Processo di distillazione continua

In a continuous distillation process, a feed mixture is separated into its components based on differences in boiling points. The system typically consists of a distillation column, reboiler, and condenser.

The process begins with the introduction of a liquid feed into the distillation column, where it is heated in the reboiler. This heat causes the more volatile components to vaporize and rise through the column. As the vapor ascends, it encounters descending liquid, facilitating mass and heat transfer between the two phases. The vapor phase becomes richer in the more volatile component, while the liquid phase becomes richer in the less volatile component. The feed condition can be represented by the equation: − ′=

The feed divides the column into two distinct regions: the enrichment zone and the stripping zone. The enrichment zone is the upper section of the column where the vapor rises, becoming increasingly rich in the more volatile components as it interacts with the descending liquid. The stripping zone is the lower section of the column where the liquid descends, allowing the less volatile components to be stripped from the liquid phase.

From the condenser and reboiler, there is reflux to enhance the separation process. Reflux is the portion of the condensed vapor that is returned to the column to provide additional cooling and improve separation efficiency.

Mass balances for the continuous distillation process can be expressed for both the entire column and for individual stages. For the overall column, the mass balance relates the input feed, the distillate, and the bottoms product:

Overall MBi:
• − = − =+ { →= + − ={ − e x are fixed, the flow rates D e R are also fixed.

If the compositions y D R

Other balances are around the condenser, the reboiler and the feed:

Condenser MBi:
• =+{ → = + = + +1

Reboiler MBi:
• ′ ′ = ′ + { → = + = ′ + ′ ′ ′′ ′ +1

Feed Mbi:
• 1 − 1 = ′ + )(1{ → → = −= + − + )(1′ = + −

In the x-y composition diagram, the x-axis represents the liquid phase composition, while the y-axis represents the vapor phase composition. The equilibrium line, typically a curve, indicates the relationship between the compositions of the two phases at equilibrium. The operating lines, which represent the mass balances around the column, are the ones just derived from the mass balance equations.

2) Variabili indipendenti nella colonna di distillazione

To determine the number of independent variables in a distillation column, we use the =N -N . However, defining the variables and method proposed by Kwauk, where NI V C constraints for the entire process can be complex. For this reason, it is more practical to divide the column into five elementary blocks:

For each unit, the degrees of freedom (DoF) can be calculated using: ∑ = + − , where are the independent variable of each unit, the operative variables for each element ( = Indip. Var. – Ind. Eq.), possible additional DoF, and the additional constraints to avoid double counting.

According to the Gibbs rule, a stream with N C components is characterized differently for monophasic and biphasic streams. In a monophasic stream, there are N −1+2=N +1C C +2 intensive variables plus one extensive variable (the flow rate), resulting in a total of N C variables. In a biphasic stream, there are N −2+2=N intensive variables along with two C C +2 extensive variables (the flow rates of the two phases), also leading to a total of N C variables.

For the condenser, we have to distinguish between a partial or a total one:

• Partial: the N +2 is for V and2( 2) ( 1)• = + + 1 − + = + 4, C 0N +2 for V+L, because it can be seen as just one stream in equilibrium; +1 is the CQ , we have N material balances and 1 energy balance.−( 1)+C C
• Total: we can see it as the sum of the total condenser plus the splitter for the reflux, • 1,+ 1,1, to avoid L double counting. So we so = + − ( + 2) 0 1,1, and have: 2( 2) ( 1) ( 2) ( 3)= + + 1 − + = + + + − , where Nc+2 is for the L the Nc+3 is for the two stream exiting from the( 1)+ 01,+ splitter. The total condenser has an additional dof, which is = + 5. the degree of reflux subcooling.

The reboiler is typically partial, so it can be treated similarly to the partial condenser.

For the generic and feed stage we can apply a similar idea and get:

For the generic stage the 33( 2) ( 1)• = + + 1 − + = 2 + 6, streams are V ,L and the equilibrium V ,L .j+1 j-1 j j3,

The same for the feed stage getting:
• = + + 2 = 3 + 8 2

So for the enrichment section made up by NP stages we obtain: (2 6) = + + ethe third term avoid double counting of the2( 1)( 2) 2( )1 − − + = + + 5 streams in common between the every couple of stages. For the same reason we obtain4 Summing up all the elementary that in the stripping section: : 2( ) = + + 5. blocks we obtain: 2( ) = + + + 10.

Usually the values of the Nc + 2 variables of the feed are known, the values of the NPe +NPs + 3 pressures (for the stages, the feed stage, the condenser and the reboiler) are given by the engineer, the values of NPe + NPs + 1 thermal duties (for the stages, the feed stage) are given, for instance by assuming an adiabatic distillation column. Therefore, only 4 degrees of freedom remain. In the case of total condenser, the constraint placed on the thermal condition of the reflux must be taken into account as an additional degree of freedom.

3) Bilancio energetico

The overall energy balance: can be divided into L and V + = + + contributions with we get: + (1 − )ℎ + = + ℎ + = + ℎ , assuming we have + ℎ + = + ℎ + ℎ + ℎ ~ℎ ~ℎ ℎ = ; then dividing by F: . ℎ + ℎ = + −

It can be noticed that if we have higher than for and vice versa. > 0 = 0, Assuming independent from composition, often true on molar basis, = ,(Trouton rule) = = = .+1

For a single stage the energy balance: + ℎ = + ℎ →+1 +1 −1 −1 , considering for the) = + − − − + − − = 0ℎ(+1 −1 +1 +1 +1 −1 MB, we obtain . = +1 +1 ( ) −, , ′

For the feed stage: )( ( )− = − = −→ , ,

This graph represents the feed conditions:

• Subcooled liquid • < 0
• Saturated liquid • = 0
• L-V mixture • < 10 <
• Saturated vapor • = 1
• Superheated vapor • > 1

4) Rapporto di riflusso

The reflux ratio, defined as r=L/D, where L is the reflux flow rate and D is the distillate flow rate, plays a crucial role in distillation design and operation.

In a design problem for a distillation process, one degree of freedom is typically used by introducing the feed at the "optimum" stage, which minimizes the total number of stages required. Additionally, it is desirable to select a reflux ratio that minimizes the overall plant cost, referred to as the "optimal" reflux ratio. After these choices, two degrees of freedom remain to be specified to fully determine the system, typically in the form of design specifications on the product compositions or purities.

In contrast, for a rating problem, the number of available stages in the enrichment and stripping sections is fixed and known. If the reflux ratio is imposed, only one degree of freedom remains. In this case, the "optimal" reflux ratio can also be chosen, but the focus shifts to maximizing the separation efficiency within the given constraints.

The optimal reflux ratio is between to limits: total reflux and minimum reflux.

For the total reflux the two operating lines coincide with the bisector and their interception coincides with F, derives that F=D=R=0, = =→ ∞. In practice this situation occurs only during the column start up, and it is useful to determine the minimum number of trays required to obtain a certain fractionation.

The minimum reflux ratio is the smallest r at which the column can separate the mixture to the desired purity using an infinite number of stages. At this value of r the operating lines intercept the equilibrium − .curve with the feed line. = −

The calculation is based on the minimization of total production costs, defined as the sum of plant (capital) costs and operating costs, per unit distillate product.

The key operating variable is the reflux ratio r, as it influences both the number of column stages and the flow rates of liquid and vapor in the column. Therefore, it seems reasonable to express both capital and operating costs as a function of r, so as to be able to find out a value of r that minimizes the total production cost.

An increase in the reflux ratio for a given production, defined by flow rates and compositions F,D, R, affects the distillation column in multiple ways. It reduces the number of stages required, resulting in a shorter column height. However, it also increases the flow rates V,V′,L,L′, which leads to a larger column diameter, approximately proportional to V . The condenser and reboiler duties rise, requiring larger 0.5 heat exchange surfaces, greater cooling water, and steam consumption. Additionally, the higher reflux flow rate increases both capital costs, such as pumps, pipes, and valves, and operating costs. These effects highlight the trade-offs involved in optimizing the reflux ratio. Usually the , with = This value can be obtained graphically knowing that the total costs of column are equal to~1,2 ÷ 1,3. the sum of the initial costs and the running costs:

5) Operazione di processo

When approaching a process operation problem, the effect of the reflux ratio on a column with a fixed number of stages (N) is primarily determined by the ratio V/F. The column considered has a very high number of ideal stages.

For a given F, a value of V (or V′) is assumed. The separation in the = 0, −x , can be maximized as a function of the reflux flow column, defined as x D B rate L at the boiling point.

The minimum reflux case corresponds to the condition where D=Dmax or R=Rmin.

For this, two possible cases arise depending on the values of V and F:

• If V>F, then Lmin=V-F, Dmax=F and Rmin=0;
• If V<F, then Lmin=0, Dmax=V and Rmin=V-F;

The maximum reflux condition corresponds to the case where D=0 and L=V.

The optimal reflux ratio (L ) must be determined through simulation and lies ∗between Rmin and Rmax. The maximum fractionation (x −x ) can be achievedD B=V-Fx when L , under the assumption of an infinite number of stages.∗ F

This means that separation into two pure products is only achievable when and at the bottom: L’-V’=R=F(1-x ).V−L=D is equal to Fx F F

Infinite stages – binary distillation:

If 0<L<L , the residue primarily contains the heavier product, while the ∗distillate is contaminated with the lighter component.

At L=L the distillate achieves maximum purity for the light component. At this ∗point, the curve is tangent to the axis, meaning small changes in L lead to significant changes in separation.

When L>L , the purity of the distillate decreases, and the lighter component ∗accumulates in the reflux.

The condition of x D=100% is only possible when approaching an infinite number of stages, making it unattainable in practice.

In the case of a finite number of stages, the separation curve flattens as N decreases, illustrating the limitations of achieving perfect separation with fewer stages. An example:

Batch distillation process

6) Processo di distillazione batch

Batch distillation is used when modest quantities (charges) of mixtures must be fractionated. In particular, batch processes are used when: the mixture to fractionate is available occasionally, since it is obtained in campaign processes or the same column is used to separate different charges at different times, these columns are therefore built