Chapter 13, Problem 13.52P

(a)

Interpretation Introduction

Interpretation:

The bubble point pressure for the given ternary system is to be calculated using NRTL equation.

Concept Introduction:

Antoine equation is used to determine the vapor pressure of any substance at the given temperature by the equation:

  $\ln P^{\text{sat}}\left(\text{kPa}\right)=A-\frac{B}{\left(T^{\circ }\text{C}\right)+C}$    ....(1)

Here, $A,B\text{ and }C$ are the constants specific for a substance given in table B.2 of appendix B.

Equation $13.19$ to be used for Modified Raoult’s law is:

  $y_{i}P=x_i{\gamma }_i{P}_i{}^{\text{sat}}$    ....(2)

The Bubble point pressure for a ternary system in vapor/liquid equilibrium is defined as the pressure where first bubble of vapor appears which is in equilibrium with the liquid present in the system. The equation which defines this pressure at this point is:

  $P_{\text{BUBL}}={\displaystyle \sum _i{x}_{\text{i}}{\gamma }_i{P}_{\text{i}}^{\text{sat}}}$    ....(3)

NRTL equation to be used for a multicomponent system is:

  $\ln {\gamma }_i=\frac{{\displaystyle \sum _j{x}_j{\tau }_{ji}{G}_{ji}}}{{\displaystyle \sum _k{x}_k{G}_{ki}}}+{\displaystyle \sum _j\frac{x_j{G}_{ij}}{{\displaystyle \sum _k{x}_k{G}_{kj}}}}\left[{\tau }_{ij}-{\displaystyle \sum _k\frac{x_k{\tau }_{kj}{G}_{kj}}{{\displaystyle \sum _j{x}_j{G}_{kj}}}}\right]$    ....(4)

Here, the parameter ${\tau }_{ij}$ is calculated by the formula:

  ${\tau }_{ij}=\frac{b_{ij}}{RT}$    ....(5)

And, $G_{ij}$ is calculated by the formula:

  $G_{ij}=\exp \left(-{\alpha }_{ij}{\tau }_{ij}\right)$    ....(6)

Where, ${\alpha }_{ij}\text{, and }{b}_{ij}$ are the NRTL equation parameters given in table $13.10$ for binary systems.

(b)

Interpretation Introduction

Interpretation:

The dew point pressure for the given ternary system is to be calculated using NRTL equation.

Concept Introduction:

Equation $13.19$ to be used for Modified Raoult’s law is:

  $y_{i}P=x_i{\gamma }_i{P}_i{}^{\text{sat}}$    ....(2)

NRTL equation to be used for a multicomponent system is:

  $\ln {\gamma }_i=\frac{{\displaystyle \sum _j{x}_j{\tau }_{ji}{G}_{ji}}}{{\displaystyle \sum _k{x}_k{G}_{ki}}}+{\displaystyle \sum _j\frac{x_j{G}_{ij}}{{\displaystyle \sum _k{x}_k{G}_{kj}}}}\left[{\tau }_{ij}-{\displaystyle \sum _k\frac{x_k{\tau }_{kj}{G}_{kj}}{{\displaystyle \sum _j{x}_j{G}_{kj}}}}\right]$    ....(4)

Here, the parameter ${\tau }_{ij}$ is calculated by the formula:

  ${\tau }_{ij}=\frac{b_{ij}}{RT}$    ....(5)

And, $G_{ij}$ is calculated by the formula:

  $G_{ij}=\exp \left(-{\alpha }_{ij}{\tau }_{ij}\right)$    ....(6)

Where, ${\alpha }_{ij}\text{, and }{b}_{ij}$ are the NRTL equation parameters given in table $13.10$ for binary systems.

The Dew point pressure for asystem in vapor/liquid equilibrium is defined as the pressure where a drop of liquid in equilibrium with the vapor present in the system at a temperature. The equation that defines this pressure at this point is:

  $P_{\text{DEW}}=\frac{1}{{\displaystyle \sum _i\frac{y_{\text{i}}}{{\gamma }_i{P}_i^{\text{sat}}}}}$    ....(7)

(c)

Interpretation Introduction

Interpretation:

  $P,T-$ flash is to be performed for the given ternary system using NRTL equation.

Concept Introduction:

Equation $13.19$ to be used for Modified Raoult’s law is:

  $y_{i}P=x_i{\gamma }_i{P}_i{}^{\text{sat}}$    ....(2)

The Bubble point pressure for a system in vapor/liquid equilibrium is defined as the pressure where first bubble of vapor appears which is in equilibrium with the liquid present in the system. The equation defining the pressure at this point is:

  $P_{\text{BUBL}}={\displaystyle \sum _i{x}_{\text{i}}{\gamma }_i{P}_{\text{i}}^{\text{sat}}}$    ....(3)

The Dewpoint pressure for a system in vapor/liquid equilibrium is defined as the pressure where first drop of liquid appears which is in equilibrium with the vapor present in the system at a temperature. The equation that defines this pressure at this point is:

  $P_{\text{DEW}}=\frac{1}{{\displaystyle \sum _i\frac{y_{\text{i}}}{{\gamma }_i{P}_i^{\text{sat}}}}}$    ....(7)

$P,T-$ flash calculations are done to find the values of $\mathcal{V}\text{, }\mathcal{L},y_i,\text{ and }{x}_i$ for a system which flashes to produce a two-phase system of vapor and liquid in equilibrium.

The equation for equilibrium ratio, $K_i$ also known as K-value is:

  $K_i\equiv \frac{y_i}{x_i}$    ....(8)

Here, $y_i$ is the vapor phase mole fraction and $x_i$ is the liquid phase mole fraction of species $i$ in the system in VLE.

The equations for flash calculationare:

  $\mathcal{L}+\mathcal{V}=1$    ....(9)

Here, $\mathcal{V}$ is the total moles of vapor and $\mathcal{L}$ is the total moles of liquid.

In terms of $K_i$, the equation relating $y_i\text{ and }{z}_i$ is:

  $y_i=\frac{z_i{K}_i}{1+\mathcal{V}\left(K_i-1\right)}$    ....(10)

Here, $z_i$ is the total mole fraction of component $i$ in the system.