FactSage Ferrous Processing - Review of Thermodynamics

Ferrous Applications – Engineering Thermodynamics 1

REVIEW OF

ENGINEERING

THERMODYNAMICS

Department of Mining and Materials Engineering


Gibbs energy

G = H – TS; G: Gibbs Energy, H: Enthalpy, S: Entropy

1. For pure elements or pure compounds (Al, O2, Al2O3, etc.)

o

T

o

T

o

TTSHG

T

K

p

o

K

o

TdTCHH

298

298

T

K

po

K

o

TdT

T

CSS

298

298

enthalpy of compound at 298 K with

reference to pure stable elemental species

At 298 K, 1 atm ( , unknown)

: Cp = a + bT + cT-2

+ dTlnT + · · ·

is known (measurable)

Standard state for H :

for all stable elements at 1atm and 298K.

Fe(bcc), Fe(fcc), Fe(l), H2O(l), H2O(g), H2(g),

O2(g), O(g), CaO, FeO, C(s), CO2, CO,.

0ΔHo

298K

standard entropy at 298 K

( ) 00

o

KS

00

o

KH

* In FactSage compound databases,

, , , are stored

Absolute Gibbs Energy of compounds

relative to elemental species.

o

298KΔH

o

KS

298 pC


Gibbs energy

2. Chemical reaction between pure compounds (No solutions)

nA + mB = AnBm

o

rxn

o

rxn

o

B

o

A

o

BArxn

STH

mGnGGGmn

)(

In many thermodynamics books, , are given.

These values are not absolute values, but dependent on each chemical

reaction.

In FactSage, therefore, absolute Gibbs energy of each species

(relative to elemental species) is stored. Then, the reaction Gibbs

energy for any reaction can be automatically calculated from the Gibbs

energy of each species.

o

rxnH

o

rxnS


Gibbs energy

3. Chemical reaction involving gas

nA + mO2(g) = AnO2m

At Equilibrium

2 2

( )n m

o o

rxn A O A OG G n G m G

i

o

iiPRTGG ln

for ideal gas species i

2

lnO

oPmRTG

0rxn

G

)ln(2

1

m

OP

oRTG


Gibbs energy

3. Chemical reaction involving gas (continued)

In general, for aA + bB(g) = cC + dD(g)

At equilibrium

)ln(b

B

d

D

P

PoRTG

KRTGo

ln K: Equilibrium constant

FactSage Reaction module can give this kind of answer

quickly. Reaction module is only for stoichiometric species

(No solutions are involved in the Reaction module

calculation)


Gibbs energy

4. Chemical reaction involving solid or liquid solutions

)ln()(ln)( i

o

pureisoiniaRTGG a: activity

change of Gibbs energy of i in solution

by interacting with surrounding species

Definition of activity

o

Ap

Pure Liquid A

Pure Gas A

A in solution

Ap

Gas Mixture

AAo

A

A

Ax

P

Pa

∴ aA is the activity of species A in solution:

higher activity means a higher chance of

evaporating.


Gibbs energy

Activity

ii

o

iiixppa )/(

0 x i 1

ia

(+) deviation

(-) deviation

ideal

1

4. Chemical reaction involving solid or liquid solutions

(+) deviation: repulsion between i and other species

: more active chemical reaction of i

(-) deviation: attraction between i and other species

: less active chemical reaction of i

iixa

iixa

In general, for aA + bB(g) = cC + dD(g)

At Equilibrium

)ln(b

B

a

A

d

D

c

C

Pa

PaoRTG

reactantsproductsrxn GGG

* FactSage solution databases contain

model parameters to calculate

ia

iG


Gibbs energy minimization

In most thermodynamics texts, one calculates equilibrium conditions

0rxn

G eq

oKRTG ln

In real calculations, we want to know the direction of reaction and

the final products

mA + nB

many possible outputs

A2B

Inputs (initial condition)

Tfinal, Pfinal

(m-2)A

(n-1)B

AB2

(m-1)A

(n-2)B

A2B (m-3)A

(n-3)B AB2

(m-x)A

(n-y)B

(xA-yB)soln

Final equilibrium state?


Gibbs energy minimization

(continued)

We have to find out which phase assemblage is most stable at given Tf

and Pf for a given mass balance (inputs).

Gibbs energy minimization routine. (ChemSage, Solgas-mix, etc.)

The most stable phase assemblage is the one with the lowest Gibbs

energy.

In FactSage

i) Input amounts

ii) Select all possible product phases (solid compounds, solid

solutions, liquid solutions, gases)

iii) Set Tfinal and Pfinal

iv) Calculation (Gibbs energy minimization routine)

v) Equilibrium phase assemblage calculated


Ellingham diagrams Δ

Go (

kJ /

mole

of O

2)

T (K)

(A)

(B)

- Collection of ΔGo values for oxidation reactions

mA + O2 = AmO2 (reference: 1 mol of O2)

- Only consider pure compounds.

(No solutions are considered.)

TpRG

pRTG

pa

aRTGG

O

o

O

o

OA

AOo

)ln(

ln

)()(

)(ln

2

2

2

2):0(, mEquilibriuG

A + O2 = AO2


Solution thermodynamics

A-B solution, (Solid or liquid solution)

( )so lu tion m o la r i iG x g

lno

i i ig g R T a gi: partial molar Gibbs energy of i in solution

( ) ( ln ln )o o

A A B B A A B Bx g x g R T x a x a

XB

mixgΔ

solutiong

o

Ag

o

Bg

AAg

BBg

A

o

AAaRTgg ln

AaRT ln

: Chemical potential of i i




1. Ideal solution:

s o ln (m o la r) ( ) ( ln ln )o o

A A B B A A B BG x g x g R T x a x a

1,1 BA


A A B B A A B BG x g x g R T x x x x

2. Regular solution: 2

lnBABA

xRT


A A B B A A B B A B A BG x g x g R T x x x x x x

Ω: Regular solution parameter

i i ia x


3. General solution: ),( TxfA

, 1

( ln ln )e x ij i j

A B A B A A B B

i j

G x x R T X X




A A B B A A B BG x g x g R T x a x a

s o ln (m o la r) ( ) ( ln ln )o o e x

A A B B A A B BG x g x g R T x x x x G

* FactSage supports many complex solution models.

Solution databases (FToxid, FTSalt, ....) contain optimized

model parameters reproducing Gibbs energies of solutions.

“Polynomial model”:

A A Aa x


Gibbs Energy and Phase Diagrams

A phase diagram shows graphically the minimum Gibbs

energy assemblages of a system.

T1

Porter, D.A., and Easterling, K.E., Phase Transformation in Metals and Alloys, 2nd Ed. CHAMAN & HALL (1992)


Gibbs Energy and Phase Diagram



T2






T3






T4



Thermodynamic Database

Development: FactSage

Pure compounds

Solution

Calorimetry

emf

Knudsen cell

Vapor pressure

emf (activity)

Knudsen cell (activity)

Vapor pressure (activity)

Solution calorimetry (enthalpy)

Phase diagrams

o

T

o

T

o

TTSHG

T

K

p

o

K

o

TdTCHH

298

298

T

K

po

K

o

TdT

T

CSS

298

298

K

K

po

KdT

T

CS

298

0

298

1, ji

j

B

i

A

ij

AB

exxxG


Dilute Solutions

: Henry’s law

0 xA 1

Aa

(+) deviation

(-) deviation

ideal

1

o

AA

A

o

Axa

A

o

A

slope

Constant slope

Henrian activity coefficient

* In FactSage, you cannot see the Henrian activity coefficient (in general,

activity coefficient) value directly, but if you calculate the activity in the

Equilib module in the very dilute composition region, you can calculate the

Henrian activity coefficient using this relationship.


Dilute Solution

Most refining processes involve impurity elements (dilute solutes)

Henrian activity is important

For example, Al-deoxidation process in steelmaking,

)()(

)(ln

)()(

)(ln

3232

3232

O

o

OAl

o

Al

OAl

OAl

OAlo

XX

aRT

aa

aRTG

o

Al is the Henrian activity coefficient of Al in pure liquid Fe

Change of from : interaction coefficients o

Al

Al

...lnln C

C

AlO

O

AlAl

Al

Al

o

AlAlxxx

)(3232

sOAlOAl

Now, if we have other elements in Fe such as O, Mn, C, etc.

there is interaction between Al and these elements.

* FactSage FTmisc-FeLQ database contains these Henrian activity

coefficients and interaction parameters for liquid steel.


Change of Standard State

)(ii

gg

Gibbs Energy

o

wtig

.%)(

o

Rig

)(

o

Hig

)(

)(ln

RiaRT

)(ln

HiaRT

%)(ln

wtiaRT

.%)(.%)(

)()()()(

ln

lnln

wti

o

wti

Hi

o

HiRi

o

Rii

aRTG

aRTGaRTGG

o

i

o

HRiRTG ln

)(

Raoultian standard state Henrian standard state

i

Bulk

o

io

wtRi

M

MRTG

100ln

%)(

Raoultian standard state 1 wt.% standard state

...ln k

k

ij

j

ii

i

iixxxf

iiHixfa

)(

...]%[]%[]%[log kwtejwteiwtefk

i

j

i

i

ii

Change of standard state is like

temperature scales, K, oC (that is, just

the zero point of lnai is changed).

FactSage doesn’t provide standard state conversions. Users

must do the conversions using the formulae above.

i (w t.% ) ia = f [ w t% i]


No direct way to do this type of calculation in FactSage.

In FactSage, (between pure species) can be calculated

from the Reaction module, and the activity of each solution species in

the reactants or products can be calculated using the Equilib module.

Then, using the above formula, we can calculate

Gibbs energy of reaction

i

o

iiaRTgg ln

reactantsiiproductsiireactiongngnG )()(

Activity of i Standard state should be checked carefully

o

reactionG

When the reactants or products are

- Pure species (not in a solution): activity = 1

- Species in solution: requires an activity value (can be calculated from FactSage)

reactionG


Heat evolution calculation

A(s) He

at (

en

thal

py)

A(L)

CP(s)

CP(l)

Hm (melting)

process H initial

H final

H = H final - H initial =


A(s)

B(s)

AB(s)

He

at (

en

thal

py)

process

Hf = heat of formation (or reaction) from A(s) + B(s) to AB(s) (typically negative value)


Hf

Negative H means

“generation of heat”


In FactSage, the H initial and H final are directly calculated because the H of each phase is calculated from the thermodynamic equations (database) of each solid or liquid phase. It is important to select proper initial and final materials states and temperatures


A(s)

B(s)

AB(s)

A-B solution (liquid)

A(L)

B(L)

He

at (

en

thal

py)

process


• Many industrial processes require mass and heat balance calculations. FactSage can provide a very easy way to do such calculations. For example, the following calculation would take several hours or days (or more) manually, but it takes less than 1 minute with the FactSage Equilib module.


Fe-Mn-Si melt (1600oC)

CaCO3 (25oC)

Fe-C ingot (500oC)

Heat loss

Final products

temperature

pressure

FactSage Ferrous Processing - Review of Thermodynamics

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