Bubble Point

Dew point

We may define the physical equilibrium constant, K_i:

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

And at these pressures the Poynting factor » 1:

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

And:

III

Given V_iX, P^Sat, solve for P total:

To find the dew point pressure at a given T and Y:

Or:

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

Find T_bp and y_i from P + X_i’s: Use III to get T_bp (unknown). P_i^Sat and V_i are known, but may require root finding program: For vapor composition:

B-3 Missing

V. Flash calculations:

All Z_i,P, and T are known; find X’s, y’s, 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:

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

P₁^Sat= 323.5 mmHg P₂^Sat= 537.1 mmHg

We also know the Von Laar coefficients:

A = 2.41 B = 1.97

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:

Wilson

Antoine’s

Wilson correlation:

We must satisfy 3 equations:

Initial guesses x₁=x₂=0.5

Solution: x₁=0.811 P=0.3443bar

Estimate T_BP and y’s for acetone (1) – water (2) mixture with x1=0.01, P = 1.013 bar.

Given: Wilson Parameter:

Without T_BP we do not know P^Sat’s!

Solution must satisfy:

Guess y’s & T_BP: Try y=0.5 T=373

Solution: y₁=0.353 T=361.6K

experimental

Estimate TDP and x’s for 0.36 mole fraction vapor ethanol (1) and hexane (2) at 1.013 bar.

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

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 _i’s

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 H_vgs!)

(I mole basis)

Since we do not know T, x’s, 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 Raoult’s Law requires an expression for P_i^Sat(T)and g _i(T).

We will also require Cp’s DH_vgs’s, (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 & P’s 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)

Y’s, V’s, P; when we calculate a P_xy 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 a_m and b_m 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: