제 6장 다상계(Multiphase –System)

1절 학습개요

 단일 성분 상 평형

 Gibbs Phase Rule(상률)

 기-액 평형계(한 성분만 응축되는 계)

 Multicomponent Gas-Liquid System

 고-액 혼합용액

 액-액 추출

제 6장 다상계(Multiphase –System)

2.1절 학습목표

 두상으로 구성된 계(system)를 설명하는 물리적 성질들과 법 칙 습득

 단일 성분으로 구성된 다상계(multiphase system)의 물성을 계산하는 방법 습득

 상법칙(phase rule)을 이해하고, 계를 해석하는데 필요한 독립적인 변수의 수를 결정하는 방법 습득

 다성분 기-액 계의 해석 및 응용(증류, 흡수, 습윤)을 습득

 다성분 액-고 계의 해석 및 응용(침출, 건조, 결정화) 습득

 두개의 서로 섞이지 않는 액체들의 해석 및 응용(액-액 추출) 습득

2.1절 학습목표(계속)

 다상 운전: 한 성분에 대한 상 변화 운전 (예: 용융, 증발, 응축, 고화 등), 혼합물로부터 상호 분리, 정제

 분리: 한 상의 혼합물을 두개 상으로 구성된 시스템에 공급.

원 공급 상에 성분 A 농축, 다른 상에 성분 B 농축, 두 상을 중력 이용

 중력 이용 분리 : 기상/액상 분리, 섞이지 않는 액상 분리

 필터, skimmer 등 장치 이용 분리

상을 이용한 분리 응용 예

^:

수용액으로부터 메탄올 회수: 증류

액체 파라핀/방향족 탄화수소 분리 : 에틸렌글리콜 이용 방향족 분리 (액체 추출)

원두 커피: 침출(고상에서 액상으로)

기체 이산화황 제거: 흡수, 혹은 탈거(scrubbing)

Isomer 분리( para-xylene(C₆H₄(CH₃)₂), ortho-xylene, meta-xylene):

- 분자체 이용 흡착(para-xylene) 분리: 기공 크기 충분 오르소,메타는 흡착되기에 기공이 작음.

- 결정화(para-xylene의 고화:13.3℃): 오르소 고화 온도=-25.2 ℃, 메타 고화온도=-47.9℃

에스테르 생산 공정 예

Distillate : azeotrope (83% ethyl acetate, 8% ethanol, 9% water), b.p.= 70℃

Extract : ethanol, water

2.2절 학습 목적

• After completing this chapter, you should be able to do following:

– Explain in your own words the terms separation process, distillation, absorption, scrubbing, liquid extraction, crystallization, adsorption, and

leaching. (What are they and how do they work?)

– Sketch a phase diagram(P versus T) for a single species and label the regions (solid, liquid, vapor, gas). Explain the difference between a vapor and a gas.

– Use the phase diagram to define (a) the vapor

pressure at a specified temperature, (b) the boiling point at a specified pressure, (c ) the normal

boiling point, (d) the melting point at a specified pressure, (e) the sublimation point at a specified pressure, (f) the triple point, and (g) the critical temperature and pressure. Explain how the melting and boiling point temperature of water

vary with pressure and how P and T vary (increase, decrease, or remain constant) as a specified path on the diagram.

– Estimate the vapor pressure of pure substance at a specified temperature or the boiling point at a

specified pressure using

(a) the Antoine equation, (b) the Cox chart, (c ) the Clausius-Clapeyron equation and known

vapor pressures at two specified temperatures, or (d) Table B.3 for water.

– Distinguish between intensive and extensive

variables, giving examples of each. Use the Gibbs phase rule to determine the number of degrees of freedom for a multicomponent multiphase system at equilibrium, and state the meaning of the value you calculate in terms of the system’s intensive

variables. Specify a feasible set of intensive

variables that will enable the remaining intensive variables to be calculated.

– In the context of a system containing a single

condensable species and noncondensable gases, explain in your own words the terms saturated vapor,

superheated vapor, dew point, degrees of superheat, and relative saturation. Explain the following statement from a weather report in terms a first-year engineering student could understand: The temperature is 75

°

F, barometric pressure is 29.87 inches of mercury and falling, the

relative humidity is 50%, and the dew-point is 54

°

_F.

– Given an equilibrated gas-liquid system containing only a single condensable component A, a correlation for , and any two of the variables y_A (mole fraction of A in the gas phase), temperature, and total pressure, calculate the third variable using Raoult’s law.

)

* ( T p_A

– For a process system that involves a single condensable component, a vapor-liquid phase change, and

specified or requested values of feed or product stream properties (temperature, pressure, dew point, relative saturation or humidity, degrees of superheat, etc.), draw and label the flowchart, carry out the

degree-of-freedom analysis, and perform the required calculations.

– Explain the meaning of the term ideal solution behavior applied to a liquid mixture of volatile species. Write and clearly explain the formulas for Raoult’s law and Henry’s law, state the conditions for which each

relationship is most likely to be accurate, and apply the appropriate one to determine any of the variables T, P, x_a, or y_a from given values of the other three.

– Explain in your own words the terms bubble point, boiling point, and dew point of a mixture of

condensable species, and the difference between vaporization and boiling. Use Raoult’s law to determine (a) the bubble-point temperature (or

pressure) of a liquid mixture of known composition at a specified pressure (or temperature) and the

composition of the first bubble that forms; (b) the dew-point temperature (or pressure) of a vapor mixture of known composition at a specified

pressure (or temperature) and the composition of the first liquid drop that forms;

(c ) whether a mixture of known amount (moles) and composition (component mole fractions) at a given temperature and pressure is a liquid, a gas, or a gas-liquid mixture and, if the latter, the amounts and compositions of each phase; and (d) the

boiling point temperature of liquid mixture of known composition at a specified total pressure.

– Use a

Txy

^or

Pxy

diagram to determine bubble- and dew-point temperatures and pressures,

compositions and relative amounts of each phase in a two-phase mixture, and the effects of varying

temperature and pressure on bubble points, dew points, and phase amounts and compositions.

Outline how the diagram are constructed for

mixtures of components that obey Raoult’s law.

– For a process system that involves liquid and gas streams in equilibrium and vapor-liquid equilibrium relations for all distributed components, draw and label the flowchart, carry out the degree-of-freedom analysis, and perform the required calculations.

– Explain in your own words the terms solubility of a solid in a liquid, saturated solution, and hydrated salt. Given solubility data, determine the saturation temperature of a feed solution of given composition and the quantity of solid crystals that form if the

solution is cooled to a specified temperature below the saturation point.

– Given a liquid solution of a nonvolatile solute,

estimate the solvent vapor-pressure lowering, the boiling-point elevation, and the freezing-point depression, and list the assumptions required for your estimate to be accurate.

– Explain the term distribution coefficient (or

partition ratio) for a solute distributed between two nearly immiscible liquids. Given feed-stream flow rates and compositions for a liquid extraction

process and either solute distribution coefficient data or a triangular phase diagram, calculate the product stream flow rates and compositions.

– Explain the term adsorption isotherm. Given

adsorption equilibrium data or an expression for an adsorption isotherm, calculate the maximum

quantity of adsorbate that can be removed from a gas by a specified quantity of adsorbent or,

conversely, the minimum quantity of adsorbent

needed to remove a specified quantity of adsorbate.

 Phase diagrams - A plot of pressure vs. temperature

Fig. 6.1-1

Phase diagrams of H₂O

and CO₂ (not drawn to scale)

3절 학습내용

1. 단일 성분 상 평형

 정의

• 기-액 평형선 위의 T, P : 끓는점, 증기압

• 1 기압에서의 끓는점 : normal boiling point

• 기-고 평형선에서의 온도 : 승화점

• 고-액 평형선 에서의 온도 : 녹는점 또는 어는점

• 기-액-고 상이 공존하는 점 : 삼중점

 증기압 예측

: Clausius-Clapeyron식

RT B p = − ∆ H^v +

∧

ln *

R : 기체상수

B : 물질마다의 고유값을 갖는 상수

∆H∧_v : 액체 단위 몰 당 증발 잠열

T : 절대온도(K)

Ex.6.1-1: 두개의 서로 다른 온도에서 측정된 증기압이 다음과 같다.

C T

C T

°

=

°

=

4 . 15

6 . 7

2 1

mmHg p

mmHg p

60 40

* 2

* 1

=

=

Clausius-Clapeyron 식의 매개 변수들을 결정하고, 이 식을 사용, 42.2℃에서 증기압(P^*) 계산.

(풀이)

-1/T vs lnP^*의 좌표계에 두 점 (-1/T, lnP₁^*) 와 (-1/T₂,lnP₁^*)를 도시하면,

B=18.69

R K

H 4213

* =

∆

-1/T lnp*

69 . 4213 18

ln ^* = − + p T

T=42.2℃=315.4K에서 p^*=207 mmHg

• Cox Chart : equal temperature reference – substance plot

1 10 10² 10³ 100

10 1 p^*

p_r^*

p^* - 증기압

p_r^* - 등온에서의 기준물질의 증 기압 (일반적으로 물)

Fig. 6.1-2. Reference substance plot for vapor pressure correlation

 Cox - Chart 만들기

i) 두개 사이의 알려진 p^* 값으로부터 여러 다른 온도들에서 대응하는 기준물질의 증기압을 찾는다.

ii) p^* vs p_r*를 log지에 그리고, 직선을 그린다.

iii) p_r*축에 대응하는 T를 그려 넣는다.

Fig. 6.1-3. Reference substance plot : temperature scale for water on abscissa.

Fig. 6.1-4. Cox chart vapor pressure plots.

 Antoine equation (실험식)

C T

A B

p^* = − + log10

Table 6-1

Antoine Equation Constant

P.640 Table B.4 참조 다른 참고문헌 참고 하여 A,B,C 값 상이