Fluid phase Equilibria

Flow Phase Equilibria

SEPARATING MIXTURES

Creating a mixture starting from individual components is a spontaneous process and doesn't require energy. Instead, separating a mixture into individual pieces is not a spontaneous process and usually it requires energy.

Separation techniques allow to treat a starting mixture to obtain products of desired amount and quality (specifications).

Recovery

Purity

The mixtures are divided in: Homogeneous (one phase) and Heterogeneous (more than one phase)

The separation of different components from a homogeneous mixture can be achieve thanks to Additional phase creation (not anymore homogeneous), also Phase creation and phase addition.

To create the second phase we can cool or heat the mixture (Thermal separation processes) or add it directly (L or V), which comes in touch with the one being analyzed. Distillation. Absorption.

The distribution of the species components in this second phase at equilibrium must be different compared to the initial one.

TYPES OF PROBLEMS

In Design Problem, the aim is to determine the size of the equipment needed to obtain a product with desired specification, starting from a given feed and operating conditions.

Sizing

In Rating Problem, the aim is to determine the characteristics of the product obtained with a given equipment starting from a given feed and operating conditions.

LIGHT AND HEAVY COMPONENTS

Let's consider a liquid feed, it passes through a valve and is subject to the evaporation phenomenon, so it's pressure drops and consequently there is a partial vaporization.

The feed, which is entering at lower pressure, has a lower temperature and about the outlet products (which are in equilibrium with each other) it is possible to see that:

1. The flow rate of vapor phase increases and the flow rate of liquid phase decreases
2. The vapor and the liquid are enriched with the less volatile component so the mole fraction of the less volatile component increases in both products

The more volatile component is called light component and it's the component with the lower boiling temperature (higher saturation pressure)

GIBBS PHASE RULE

To know how many degrees of freedom a system has in thermodynamic equilibrium, so how many intensive variables can be changed independently without altering the number phase present

Variance: V = NC - NP + 2

2-D PLOTS

Isothermal plot

T constant

Let us consider a mixture with composition z when the system is at some conditions which correspond to those inside the lens. It is obtained a separation into two phases: one is a liquid and has composition x while the other one is a vapor and has composition y

Isobaric plot

P constant

Increasing the pressure, the lens shrinks and the temperature range increases

The difference between the starting mixture and the two generated phases decreases, so P negatively affects separation - more stages are required to reach the desired purity

Composition diagram (x-y)

The concentrations (x-y) in the isobaric plot are used to create the composition plot

Ideal system (Benzene+Toluene)

When the system is not ideal the bell of the curve is not perfectly symmetrical (Ethanol and water)

Azeotrope point

At azeotrope point the mole fraction x is equal to the y one and the distillation stops (x_R=y_R)

After that point the lighter component becomes the higher and viceversa

Vapor with y > x

Vapor with y < x

It is enriched with (1-x) - comp. more vola

Positive azeotrope

Negative azeotrope

VAPOR AND LIQUID EQUILIBRIUM (DoF = 2)

VLE can be calculated with mathematical models, made by EQUATIONS and PARAMETERS

mathematical description of the phenomenon

Represent how the generic behaviour is characterised for a specific system

The condition of thermodynamic equilibrium can be expressed by ISOPOTENTIAL EQ.

mu_i^α = mu_i^β = mu_i^l

phases at equilibrium

chemical potential of component in the mixture

In our case: mu_i^V = mu_i^L NC independent equation

The chemical potential can be expressed as a function of fugacity or activity

For the vapor phase only fugacity can be used

mu_i^V = mu_i^L

f_i^V

f_i^L

phi-phi APPROACH

gamma-phi APPROACH

1) phi-phi approach

From isopotential definition it is reached the ISOFUGACITY CONDITION

Fugacity is a function of T, P, composition (x₁, x₂.. x_N) and Nature of the species (methane, ethane,...)

f_i = P z_i phi_i

at the equilibrium phi_i^V y_i = phi_i^L x_i

Fugacity coefficient expresses the deviation of ideality, f (T, P, composition)

lim phi_i = 1 ideal gas nature at low P

At low P (e.s. 10 atm) f_i^V = p y_i

For vapor phase

phi_i != 1

Always for liquid phase

We calculate the fugacity coefficient with an equation of state (e.g. SRK...) CUBIC

2) gamma-phi approach

This approach uses fugacity for the vapor phase and activity for the liquid one

mu^v = mu^l => phi_iv P y_i = phi_i^*l gamma_i x_i

activity coefficient expresses the deviation of ideality

Fugacity at reference state of liquid phase (Pure component, P and T of the system)

phi_i^*l = phi_i^*l,sat psi_i

POINTING FACTOR

phi_i^*l,sat = f_i^*v,sat = phi_i^*v,sat p_i^sat

At the end it is obtained the following formula: phi_iv P y_i = phi_i^*v,sat p_i^sat psi_i gamma_i x_i

In order to calculate psi_i, we need to use a model. The activity coefficient is equal to 1 for ideal liquid mixtures and for pure component, while is < 1 for non-ideal mixtures and diluted systems

When x_i -> 1 the species i is more likely to interact with other molecules of i so the behavior is close to ideality

lim gamma_i = 1

x_i->1

When x_i -> 0 the species i is extremely diluted, so it is more likely that the molecules interact with other species molecules, that's a non ideal behavior

lim gamma_i = gamma_i⁰ != 1

x_i->0

psi_i is equal to 1 when the pressure is lower than 50/100 bar of vapor phase

phi_iv and phi_i^*v are calculated using a EoS, their value is unity for low pressure

So we end up with: phi_iv P = p_i^sat gamma_i x_i

ideal mixture

P y_i = p_i^sat x_i Raoult- Dalton Equation

BUBBLE curve

Changing gamma_i, x_i, P we obtain the y values

Plotting P vs y the dew curve is defined

When a component of the mixture is noncondensable gas (T > Tc,i) it does not have a saturation pressure p_i^sat

A very volatile and insoluble component

Operating temperature above its critical temperature so the species i can't become liquid

At infinite dilution lim_x->0 p₁/x = H₁

Henry constant

p₁ = H₁ x    Henry law

Is a way of modeling the fugacity of a component in the liquid phase at very low concentration (infinite dilution)

Permanent gas in a liquid phase

For condensable component: H₁ = gamma₁^∞ p₁^sat

We take the tapent of fugacity curve when x->0The slope of that line is H_i

In that region we can only use the Henry law

Infinite dilution of component 1

Infinite dilution of component 2

CALCULATION OF VLE FOR A BINARY SYSTEM

Let's introduce the equilibrium ratios K_i = phi_i^l/phi_i^v

phi - phi approach

K_i = phi_i^l x_i,sat p_i^sat gamma_i^l / phi_i^v

gamma - phi approach

At low pressures phi_i^l = phi_i^v = 1

By Gibbs phase rule Dof is equal to 2: so two variables must be fixed

ABSORPTION AND STRIPPING PROCESSES

(Not thermal separation processes) -> Addition of the second phase

1 ABSORPTION

A liquid solvent is added to remove one or more components from a vapor phase

2 STRIPPING

A vapor phase is added to remove one or more components from liquid phase

3 Liquid-liquid extraction

A second liquid is added to remove one or more components from a liquid phase

1 ABSORPTION (physical)

The liquid solvent is preferably non volatile

The absorption can be either physical or chemical

Gas Liquid

Species B is removed from the gas stream because it has a much higher solubility in the liquid than are the other species in the gas

Ar pollution

Species B reacts with the solvent and remains in solution

Partial condensation

A second separation step is needed to recover the solvent

Example: Air with pollutant (sovereign) -> With a thermal separation we could obtain a condensate of P, but we have to reach a specific temperature for the condensation -> T?

To find T we need the vapour pressure conditions (P-x-y)

P_y = P_i^sat y_i x_i K_i

Since the air doesn't condense, we could assume that in the liquid phase there is only IP, so y_i = x_i = 1