Volumetric Properties of Pure Fluid
Application of
The Virial Equation
Prepared By : Agung Ari Wibowo ST., M.Sc
Thermodynamics
State Polytechnic of Malang 2017
Ideal Gas and Real Gas
Ideal Gas Real Gas
V1V2
What are the differences?
Ideal Gas
β’ No molecular interactionβ’ Exist at Low Pressureβ’ PV = RT
Real Gas
β’ Molecular interactionβ’ Compressibility Factorβ’ PV = ZRT
Compressibility Factor
RT
BP
RT
PVZ 1
21
V
C
V
B
RT
PVZ
ππ
πππ
= π΅β² + 2πΆβ²π + 3π·β²π2 +β―
π ~1
π
Z of Gas Methane at Various Temperature
Virial Equation :
Virial Equation
21.
V
C
V
B
RT
PVZc
Calculate V and Z for Isopropanol gas at 200 C and 10 Bar. By the following equation : a. Ideal Gas
RT
BP
RT
PVZb 1. B = -388 cm3/mol
C = -26.000 cm6/mol2
Virial Equation
a. Ideal GasPV = RT Z = 1V = RT/P
=83,14 cm3bar/mol Kβ 473,15 K
10 πππ
= 3934 cm3/mol
V = 3934 -388= 3546 cm3/mol
RT
BP
RT
PVZb 1.
π =π π
π+ π΅ Lihat perbedaannya !!
V1 > V2 , disebabkan oleh ZZ2 = 1- 0,099 = 0,901
V1
V2
Virial Equation
21.
V
C
V
B
RT
PVZc
π =π π
π1 +
π΅
π+
πΆ
π2
π = 3934 1 +π΅
π+
πΆ
π2
Perlu dilakukan iterasiTebak nilai V awal = V gas idealV0 = 3934 cm3/mol
Masukan ke persamaan = 3934 1 +π΅
π+
πΆ
π2
V1 trial 1 = 3934 1 +β388
3934+
β26000
39342= 3539 cm3/mol
Check apakah sama dengan V0 , ternyata tidak sama
V2 trial 2 = 3934 1 +β388
3539+
β26000
35392= 3495 cm3/mol
Diulang terus sampe Vn = Vn-1
V = 3488 cm3/mol
Cubic Equation of State
Van Der Waals EOS
Proposed by J.D van der Waals 1873
π =π π
π β πβ
π
π2
βa and b are positive constantβ
Given values of a and b for a particular fluid, one can calculate P as a function of V for various values of T c
c
c
c
P
RTb;
P
TRa
864
27 22
A Generic Cubic EOS
π =π π
π β πβ
π(π)
(π + ππ)(π + ππ)
β’ π πππ π have same value vor all substance
β’ π π are temperature dependent, and different
for each EOSβ’ b also dependent parameter and different for
each EOSEOS :1. Van der Waals2. Redlich/Kwong (RK)3. Soave/Redlich/Kwong (SRK)4. Peng/Robinson (PR)
A Generic Cubic EOS
π =π π
π β πβ
π(π)
(π + ππ)(π + ππ)
π π = ππ(ππ)π
2ππ2
ππΆ
π = Ξ©π ππΆππΆ
EOS Calculation :
Value of Tc , Pc, and π are listed in App. B
ππ =π
ππΆ; ππ =
π
ππΆ
A Generic Cubic EOS
EOS Calculation Liquid:
PV = ZRT
Generalized Equation for Gases
Pitzer Correlation
The most well known correlation related with EOS, is correlation developed by Pitzer and coworkers :
a. Compressiblity Factor (Z)b. Second Virial Eq (B)
Pitzer and Curl correlation (1955, 1957)
10 ZZZ
Dimana Z0 dan Z1 fungsi (Tr=T/Tc) dan (Pr=P/Pc)
The values can be determined from The Lee/Kesler Gener
alized-correlation Tables (Lee and Kesler, AIChE J., 21, 5
10-527 (1975) provided in App. E, p. 667
Compressibility Factor :
Pitzer Correlation
Second Virial Eq Correlation
π = 1 +π΅π
π π
Original Form :
π = 1 + αΈππππ
By Correlation:
αΈ=π΅ππΆ
π ππΆ
αΈ =π΅0 + ππ΅1
π΅0 = 0.083 +0.422
ππ1.6
π΅1 = 0139 +0.172
ππ4.2
Pitzer Correlation:
Generalized Correlation
Third Virial Eq Correlation
π = 1 + π΅π + πΆπ2
Original Form :
π = 1 + αΈπππππ
+ Δπππππ
Δ =πΆ0 + ππΆβ²
πΆ0 = 0.01407 +0.024322
ππβ
0.00313
ππ10.5
By Correlation:
π =1
π
Δ =πΆππΆ
2
π 2ππΆ2
πΆβ² = β0.02676 +0.05539
ππ2.7 β
0.00242
ππ10.5
Generalized Equation for Liquids
Generalized Correlation for Liquids
Generalized correlation for liquids
Rackett equation (Racket, J. Chem. Eng. Data, 15 (1970) 514-517:
estimation of molar volume of saturated liquids)
Lyderson, Greenkorn and Hougen:
estimation of liquid molar volume
With accuracy of 1-2%ππππ‘ = ππΆππΆ(1βππ)
0.2857
ππ =π
ππ=ππΆπ
π2 = π1ππ1ππ2
If we know T1 we can evaluate ππ1
EOS Application
In Calculation of process design, estimation of fluid properties is a must.
To choose the most suitable methods, here is the guide
EOS Application
EOS Application