Bubble Point

Dew point

We may define the physical equilibrium constant, Ki:

At lower pressures (<10 bar) the fugarity coefficients in each phase are nearly equal:

And at these pressures the Poynting factor » 1:

 

 

  1. To find the bubble point pressure at a given,T, and composition, X, we know:
  2. I

    II

    And:

    III

  3. Given ViX, PSat, solve for P total:
  4. To find the dew point pressure at a given T and Y:

    IV

    Or:

    V

     

    Solve IV for X1, and then V for P, since Vi=f(xi) This may have to be done iteratively.

  5. Find Tbp and yi from P + Xis: Use III to get Tbp (unknown). PiSat and Vi are known, but may require root finding program: For vapor composition:

 

 

B-3 Missing

 

 

 

V. Flash calculations:

All Zi,P, and T are known; find Xs, ys, and V,L

 

Here:

And:

Therefore, for each component:

 

 

 

Plus:

 

 

We must iteratively find the roots which satisfy all of the n + l equations.

Example Calculations:

  1. Find the bubble pt. Pressure and vapor composition for a liquid mixture of ethanol (1) n hexane (2) at 331 K, X1=0.412.
  2. P1Sat = 323.5 mmHg P2Sat = 537.1 mmHg

    We also know the Von Laar coefficients:

    A = 2.41 B = 1.97

  3. Find the dew pressure and liquid composition in equilibrium with a 0.314 mole fraction nitromethane vapor, y1) in carbon tetrachloride at 318K. The Wilson parameters are:
  4. Wilson

    Antoines

    Wilson correlation:

     

     

     

     

    We must satisfy 3 equations:

    Initial guesses x1=x2=0.5

    Solution: x1=0.811 P=0.3443bar

  5. Estimate TBP and ys for acetone (1) water (2) mixture with x1=0.01, P = 1.013 bar.
  6. Given: Wilson Parameter:

    Without TBP we do not know PSats!

    Solution must satisfy:

    Guess ys & TBP: Try y=0.5 T=373

     

    Solution: y1=0.353 T=361.6K

    experimental

  7. Estimate TDP and xs for 0.36 mole fraction vapor ethanol (1) and hexane (2) at 1.013 bar.
  8. Wilson Parameters:

    Criteria that must be satisfied:

    Now with x1, x2, and T unknown. (Roots found are sensitive to initial guesses)

    If we guess x=0.5 T=350K

    Solution: x1=0.555 T=332.1K

  9. Flash Calculations

A 40 mol% isobutane 160 mol%n n-pentane mixture flows into a flash chamber ad flashes at 49° C and 3.2 bar. Find how much gas and liquid leave per mole of feed, and find the composition of both streams.

Here:

Determine K is

Also

 

 

 

Choose a basis of 1 mole feed/s. Here we must solve the following criteria:

Guess a value for V, solve for x1 and x2 from 1 & 2: Determine if this satisfies 3. (A table may help)

Solution:

L = 0.8 x1 = 0.33 x2 = 0.67

V = 0.2 y1 = 0.67 y2 = 0.33

All of these methods become easy with root finding methods. (See MathCad handout)

 

Adiabatic Flash

Here the energy balance must be used in conjunction with the mass balance and equilibrium criteria! (remember Hvgs!)

 

(I mole basis)

 

Since we do not know T, xs, or V we must solve the equation A in conjunction with the previous flash criteria.

Here:

For a binary system this gives us 4 equations and 4 unknowns. Also the modified Raoults Law requires an expression for PiSat(T)and g i(T).

 

 

 

 

 

We will also require Cps DHvgss, (rigorously as f(T), but seldom all available.) Then we may solve the 4 equations iterativey until the proper roots are found.

Phase Equilibrium from EOS

Extrapolation of the activity coefficient approach to highter T & Ps may not be possible since:

We may no longer ignore and The

Poynting factor. Instead we might directly use fugacity coefficients for both phases, and .

At equilibrium:

Here, we have 5 unknowns: (for binary)

Ys, Vs, P; when we calculate a Pxy diagram:

To find the molar volumes: (using Redlich-Kuvorg)

There will be 3 roots: liquid v, vapor v, and an "unreal" middle root.

We typically use mixture rules to get am and bm for the EOS to find these roots. This allows us to solve the fugacity forms of the EOS for and . Finally, for a binary mixture we must satisfy the criteria:

1

2

Starting at , , we may determine the entire composition pressure diagram. We may similarly substitute for flash calculations.

Multicomponent Mixture

Both the Wilson an NRTL equations are readily extended to manyu components.

Example: Find the dew point pressure and liquid phase mole fractions for a vapor mixture of acetone (1), methylacetate (2), and methanol (3) at 323K.

Given:

We also need 6 Wilson parameters to determine a ternary mixtures properties.

From aijs for each binary composition:

Start B-16