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Section summary |
---|

1. Liquid Vapor
Equilibrium |

2. Calculation of
Liquid and Vapor in equilibrium |

When performing a liquid / vapor calculation, the characteristics
of the infeed are available (flow rate and composition) while the
characteristics of the vapor phase and liquid phase must be
calculated (flow rate and composition). For solving this calculation
it is also required to fix the conditions of the phases and / or
pressure and / or temperature depending on what needs to be
calculated.

For such a system, the following relations can be established

**A = V + L**

With

A = flowrate of infeed (mol/s, can be also kg/s if expressed in
mass fraction)

V = flowrate of vapor (mol/s or kg/s)

L = flowrate of liquid (mol/s or kg/s)

**A.z _{i} = V.y_{i} +
L.x_{i}**

With

z_{i} = molar or mass fraction of component i in the infeed

y_{i} = molar or mass fraction of component i in the vapor

x_{i} = molar or mass fraction of component i in the liquid

Also

Ki = y_{i}/x_{i}

**y _{i} = K_{i}.x_{i}**

With

K_{i} = equilibrium coefficient for component i

**In the 1 ^{st} case studied, the infeed is purely liquid
at its bubble point** (which means it is just at saturation, but
no phase change has happened yet, the infeed is only liquid).

z_{i} = x_{i} (no vapor
phase)

y_{i} = K_{i}.x_{i}
(general equilibrium expression) ⇒ y_{i} = K_{i}.z_{i}

Σ K_{i}.z_{i} = 1

P is given

It is then necessary to have a model to calculate the equilibrium
coefficient. It
can be quite simple if the mixture is ideal (K_{i} = P_{i}^{S}
/ P) or more complex and require
an equation of state. in any case, it is necessary to estimate
the temperature to perform the calculations as K_{i} = f(T).

The following calculation procedure is then applied :

- Estimate the temperature T
- Calculate K
_{i}= f(T) - Calculate Σ K
_{i}.z_{i} - If Σ K
_{i}.z_{i}= 1,**T is correct and equal to the bubble temperature of the mixture** - If Σ K
_{i}.z_{i}≠ 1, T needs to be recalculated by assuming a new value and going through the calculation procedure again

In the 2^{nd} case studied, the infeed is purely gaseous at
its dew point (which means it is just at saturation, but no phase
change has happened yet, the infeed is only vapor). The Engineer
wants to know what is the temperature corresponding to the dew
point.

z_{i} = y_{i} (no
liquid phase)

y_{i} = K_{i}.x_{i}
(general equilibrium expression) -> z_{i} = K_{i}.x_{i}
⇒ x_{i} = z_{i}/K_{i}

Σ x_{i} = 1

Σ z_{i}/K_{i} = 1

P is given

It is then necessary to have a model to calculate the equilibrium
coefficient. It can be quite simple if the mixture is ideal (Ki = P_{i}^{S}
/ P) or more complex and require an equation of state. in any case,
it is necessary to estimate the temperature to perform the
calculations as K_{i} = f(T).

The following calculation procedure is then applied :

- Estimate the temperature T
- Calculate K
_{i}= f(T) - Calculate Σ z
_{i}/K_{i} - If Σ z
_{i}/K_{i}= 1, T is correct and equal to the bubble temperature of the mixture - If Σ z
_{i}/K_{i}≠ 1, T needs to be recalculated by assuming a new value and going through the calculation procedure again

In a flash drum, the conditions of the infeed are such that, when
it arrives in the flash vessel **at a lower pressure**, it
separates immediately in 2 phases in equilibrium.

A.z_{i} = V.y_{i} + L.x_{i
}(general mass balance)

y_{i} = K_{i}.x_{i }(equilibrium)
-> A.z_{i} = V.K_{i}.x_{i} + L.x_{i}⇒
**x _{i} = A.z_{i} / (V.K_{i} + L)**

**Σ x _{i} = 1 = Σ [A.z_{i}
/ (V.K_{i} + L)]**

P is given

An iterative calculation is then required

- Estimate the liquid flow L
- Calculate V = A - L
- Calculate K
_{i}and Calculate x_{i} - If Σ x
_{i}= 1, L is correct and the flash calculation is done - If Σ x
_{i }≠ 1, a new value of L needs assumed and the calculation re-run

The method above works well when Ki = P_{i}^{S}/P
and therefore only depends on the pressure and temperature. If it is
not the case, then it is required to have another iteration loop
after step 3. After calculating x_{i} and y_{i}, the
coefficient K_{i} is recalculated. If it gives the same x_{i}
as 1st calculated, then we can go to step 4, if not K_{i} is
calculated again with the new composition values until it converges.