FlowingSystems

7/30/2019 FlowingSystems

1/13

Lecture 4: Phase Equilibrium in Flowing Systems1

Lecture 4: Phase Equilibrium in Flowing Systems

In this lecture well show:

How to apply thermodynamics to flowing systems

Energy and entropy balances in flowing systems

Availability and lost work

Gibbs Phase Rule for flowing systems and system specification

How data of mixture compositions are sometimes tabulated graphically.

Graphical determination of vapor-liquid equilibrium of hydrocarbon systems

Last lecture primarily focused on the thermodynamics of separations.

We covered:

Phase Stability and the Gibbs phase rule.

A simple separation based on a vapor-liquid phase diagram.

The lever rule.

Equilibrium ratios (K-values, distribution coefficients, etc.).

The activity, and activity coefficients.

Measures of separations.


2/13


Separation System Flows

Streams in

We can use the tools of entropy, energy, availability and mass balances to analyze

any separations system:

...

...

...

...

Streams out

Heat in and heat out

Work in and work out

n, zi, T, P, h, s, b, v

For each stream:

n: molar flow rate

zi: composition variables

T: temperature

P: pressure

h: enthalpy

s: entropy

b: availability

v: specific volume

(ws)in (ws)out

Qin Qout

n, zi, T, P, h, s, b, v

T0


3/13


Balances and Availability

Energy balance: nh Q Ws out

nh Q Ws in

0

Entropy balance: ns Q

Ts

out

ns Q

Ts

in

Sirr

Availability balance: nb Q 1T0Ts

Ws

in

nb Q 1T0Ts

Ws

out

LW

b h T0sAvailability:

Availability balance: Combine entropy balance, and energy balance

with the definitions for lost work and availability.

Lost work: LW T0Sirr

Minimum work: nb

out

nbin

WminThe minimum workfor a separation is

the change in availability carried by the

feed and product streams.

Availability: the energy available in the system

for conversion to shaft work.


4/13


Gibbs Phase Rule

F C 2

The number of thermodynamic conditions that can be specified for a system with C components

with phases in equilibrium.

Variables: Equations:

P

T

C (composition of each phase) C(-1)

C +2 C(-1) +

Xii

1

ki,

Xi

Xi

Note that the Gibbs phase rule does not deal

with flow variables or extensive variables.

K-values are equations

determined by

thermodynamic

equilibrium

To extend the Gibbs Phase Rule to flow systems requiresAdding: Feed stream and extensive variables

Adding: Independent equations relating variables


5/13


Gibbs Phase Rule

F C 2

The number of thermodynamic conditions that can be specified for a system with 3 components

with 3 phases in equilibrium.


T, P,

X1, X2, X3Y1, Y2, Y3Z1, Z2, Z3

Xii

1

Yii

1

Zii

1

k1v,L

Y1v

Z1L

k2v,L Y2

v

Z2L

k3v,L

Y3v

Z3L

k1v,S

Y1v

X1S

k2v,S Y2

v

X2S

k3v,S

Y3v

X3S

Mole Fractions Equilibrium Conditions


6/13


Gibbs Phase Rule for a Flowing System

The number of thermodynamic conditions that can be specified for a system with 3 components

with 3 phases in equilibrium.


T, P,

X1, X2, X3 ...Y1, Y2, Y3 ...

Z1, Z2, Z3 ...

Xii

1

Yii

1

Zii

1} C

F, Zi , TF , PF

V, L, ...

Q

}

C

C 4

C 2

Additional

Original

ki, Xi

Xi C 1

Fzi Vyi Lxi ... C

Fhf Q Vhv Lhl ... 1

C C

C1

F C 2

F 3

F C 5For a flow system:

Original

Additional

}


7/13Lecture 4: Phase Equilibrium in Flowing Systems7

Determination of Unspecified Variables

F, T, P, TF , PF , ZiF C 5If variables are used to specify

Then remaining C 1 1 variables must be found from

A) mole fraction summations

B) K-Value relationships

C) Mass balances

D) Energy balance

1 CC

1


8/13Lecture 4: Phase Equilibrium in Flowing Systems8

DePriester

In order to carry out an analysis of a separation which uses differences in

K-values between two phases to cause a separation, we need a source of

K-values.

A lot of equilibrium (K-Value) information forbinary systems is

often contained in vapor-liquid phase diagrams.

Forhydrocarbon systems, interactions between molecules are very similar,

and consequently, the K-Values will not be a function of composition. K-Values

at different pressures and temperatures for hydrocarbons can thus be graphed

for multicomponent systems.

One type of these graphs is called DePriester charts.

Another type showing vapor-liquid equilibria for a multicomponent hydrocarbon

system is shown in Figure 2.8 of the text.


9/13Lecture 4: Phase Equilibrium in Flowing Systems

9

DePriester Charts: Low T



10

DePriester Charts: High T



11

DePriester Charts: High T



12

DePriester



13

Summary

In this lecture we discussed:

How to carry out energy and entropy balances in flowing systems Availability and lost work

Gibbs Phase Rule for flowing systems and system specification

How to use DePriester charts to determine k-values for hydrocarbon vapor-liquid systems

F C 5

Next Lecture will focus on:

Isothermal Flash calculations

Derivation of the Rachford-Rice Equations

Use of Newtons Iterative method to solve the RR equations

An example using the RR procedure with Newtons method

and DePriester charts to describe equilibrium

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