PTT108 MATERIAL AND ENERGY BALANCE Chapter 5 Single Phase Systems

1. PTT108 MATERIAL AND ENERGY BALANCEChapter 5Single Phase Systems Madam NoorulnajwaDiyana

2. Introduction • Before carrying out a complete material balance, we usually need to determine various physical properties of materials in order to derive additional relationship among the system variables. • As an example we need the density to relate the volumetric flow rate to mass flow rate or vice versa. • 3 ways to obtain the values of physical properties (such as density, vapor pressure, solubility, heat capacity, etc) • Handbook or database - Perry’s Chemical Handbook, CRC Handbook of Chemistry & Physics, TRC Database in Chemistry & Engineering, etc • Estimation usingempirical correlations • Experimental work

3. Density of Liquid and Solid • Temperature dependence: modest but sometimes important (liquid and solid expanded during heating and density decrease) • Pressure dependence: usually negligible (solid and liquid are incompressible with pressure). • 2 methods to estimate the density of mixture which consist n liquid (n is number of different type of liquid) • Method 1: Volume Additivity Works best for mixture of liquid species with similar molecular structure • Method 2: Average Pure Component Densities

4. Ideal Gases • Equation of state • Relates the molar quantity and volume of a gas to temperature and pressure. • Ideal gas equation of state • Simplest and most widely used • Used for gas a low pressure and high temperature • Derived from the kinetic theory of gases by assuming gas molecules • have a negligible volume; • Exert no forces on one another; • Collide elastically with the wall of container or • The use of this equation does not require to know the gas species: 1 mol of an ideal gas at 0˚C and 1 atm occupies 22.415 liters, whether the gas is argon, nitrogen, mixture of propane and air, or any other single species or mixture of gases

5. Ideal Gas Equation of State P = absolute pressure V = volume of the gas n = number of moles of gas R = gas constant which the unit depend on unit of P, V, n, T T = absolute temperature • Ideal gas equation of state can also be written as Which ; specific molar volume of gas. • Unit for gas constant, R or

6. Ideal Gas Equation of State • Density of ideal gas (M is average molecular weight-refer back previous chapter Eq. 3.3-7) Rule of thumb for when it is reasonable to assume ideal gas behavior. • Let Xideal be a quantity calculated using ideal gas equation of state (X can be pressure, volume, temperature or mole). • Error is estimated value is ε • Let’s say quantity to be calculate is ideal specific molar volume, • If error calculated satisfies this criterion, the ideal gas equation of state should yield an error less than 1%

7. Class Discussion Example 5.2-1

8. Standard Temperature and Pressure (STP) • A way to avoid the use of gas constant, R when using ideal gas equation • For ideal gas at arbitrary temperature, T and pressure, P • For the same ideal gas at standard reference temperature, Ts and standard reference pressure, Ps (refer to STP). • Divide eq. 1 to eq. 2 • Value of standard conditions (Ps, Ts, Vs) are known, above equation can be used to determine V for a given n or vice versa • Standard cubic meters (SCM) : m3 (STP) • Standard cubic feet (SCF) : ft3 (STP) • Let say 18 SCMH mean 18 m3 (STP)/h

9. Standard Conditions for Gases System Ts Ps Vs ns Vs SI 273K 1atm 0.022415 m3 1 mol 22.4 m3/kmol cgs 273K 1atm 22.415 L 1 mol 22.4 L/mol English 492˚R 1atm 359.05ft3 1 lb-mole 359.05 ft3/lb-mole

10. “ Saya pasti akan berjaya kerana saya telah kehabisan benda-benda yang tidak berjaya” Thomas Edison

11. Class Discussion Example 5.2-2

12. Class Discussion Example 5.2-3

13. Class Discussion Example 5.2-4

14. Ideal Gas Mixture • Suppose nA moles of species A, nB moles of species B, nc moles of species C and so on, contained in a volume, V at temperature, T and pressure, P • Partial pressure, pA • The pressure that would be exerted by nA moles of species A alone in the same total volume, V at the same temperature, T of the mixture. • Pure component volume, vA • The volume would be occupied by nA moles of A alone at the same total pressure, P and temperature, T of the mixture. • Ideal gas mixture • Each of the individual species component and the mixture as whole behave in an ideal manner

15. Ideal Gas Mixture • Dalton’s Law • The summation of partial pressure of the component of an ideal gas mixture is equal to total pressure • Amagat’s Law • Volume fraction = vA/V; percentage by volume (%v/v)= (vA/V )x 100% • For an ideal gas mixture, the volume fraction is equal to the mole fraction of the substance: 70% v/v C2H6 = 70 mole% C2H6

16. Class Discussion Example 5.2-5

17. Equation of State for Nonideal Gases • Critical temperature (Tc)- the highest temperature at which a species can exist in two phases (liquid and vapor), and the corresponding pressure is critical pressure (Pc) • Other definition: highest temperature at which isothermal compression of the species vapor results in the formation of a separate liquid phase. • Critical state- a substance at their critical temperature and critical pressure. • Species below Pc: • Species above Tc-gas • Species below Tc-vapor • Species above Pc and above Tc-supercritical fluids

18. Virial Equation of State • Virial equation of state B,C,D- second, third, fourth virial coefficient respectively • Truncated virial equation Tr=T/Tc ω – acentric factor from Table 5.3-1 Tc,Pc from Table B.1

19. Class Discussion Example 5.3-1

20. Kebebasan tanpa tanggungjawab membawa kehancuran

21. Cubic Equations of State • Refer as cubic equation because when the equation is expanded, it becomes third order equation for the specific volume • To evaluate volume for a given temperature and pressure using cubic equation of state, we need to do trial and error procedure. • Two famous cubic equation of state • Van der Waals equation of state • Soave-Redlich-Kwong (SRK) equation of state

22. Van der Waals Equation of State (a/V2) - account for attractive force between molecules b - correction accounting for the volume occupied by the molecules themselves

23. Soave-Redlich-Kwong (SRK) equation of state

24. Class Discussion Example 5.3-2

25. Compressibility Factor Equation of State or If z=0, equation become ideal gas equation of state • Value of z is given in Perry’s Chemical Engineering Handbook pg. 2.140- 2.150. • Alternatively; can use generalized compressibility chart • Figure 5.4-1 – generalized compressibility chart • Fig. 5.4-2 to Fig. 5.4-4 – expansion on various region in Fig. 5.4-1

27. Step to Read Compressibility Factor • Find Tc and Pc • If gas is either Hydrogen or Helium, determine adjusted critical temperature and pressure from Newton’s correction equation • Calculate reduce pressure and reduce temperature of the two known variables • Read off the compressibility factor from the chart

28. Class Discussion Example 5.4-2

29. Nonideal Gas Mixtures • Kay’s Rule: estimation of pseudocritical properties of mixture as simple average of pure a component critical constants Pseudocritical temperature (Tc’) Tc’= yATcA + yBTcB +…… Pseudocritical pressure (Pc’) Pc’= yAPcA + yBPcB +…… Pseudocritical reduced temperature (Tr’) Tr’= T/Tc’ Pseudocritical reduce pressure (Pr’) Pr’= P/Pc’ Compressibility factor for gas mixture, Zm

30. Class Discussion Example 5.4-3

31. ANY QUESTION?