비열비(k)와 Gas Constant(C) 관계

gas/vapor 의 안전밸브  sizing에 사용되는 비열비(k)와 Gas Constant(C)에 대한 관계식을 공유하고자 한다.

 

 

 

비열비(k)와 Gas Constant(C) 관계

ASME boiler, Pressure Vessel Code, API and ISO recommended practices and standards에 의한 안전밸브 sizing 절차에 따라 안전밸브 오리피스 크기를 계산한다.

 

 

orifice sizing for vapors or gases 

증기 또는 가스의 오리피스 사이징은 용량 중량(capacity weight)  또는 체적 유량(volumetric flow rates) 두가지 방식으로 할 수 있다. 사용되는 공식은 완전 기체 법칙을 기반으로 한다. 즉, 기체가 열을 얻거나 잃지 않으며(단열), 팽창 에너지가 운동 에너지로 변환된다고 가정한다.

그러나 이러한 방식으로 작동하는 기체는 거의 없으며, 기체가 포화 상태에 가까워질수록 완전 기체 법칙과의 편차가 커지므로, 크기 조정 방정식에는 기체 상수(C) 및 압축성 계수(Z)와 같은 다양한 보정 계수가 포함되어 완전 기체 법칙으로부터의 편차를 보정하고 있다. 

 

 

1. Metric units

	set pressures ≥ 1.03 barg	set pressures < 1.03 barg or Vacuum conditions
Weight flow  (kg/hr)
Volumetric flow  (nm3/hr)
where	A  = Minimum required discharge area, ㎟ C =  gas constant based upon the ratio of specific heats of the gas or vapor at standard conditions. (use C = 2.390 if ratio of specific heats is unknown) K = Coefficient of discharge.  Kb = back pressure correction factor for gas.  Kc = Combination factor for installations with a rupture disc upstream of the valve. (use a 0.9 value for any rupture disc/pressure relief valve combination not listed, and use a 1.0 value when a rupture disc is not installed) M= Molecular weight of the gas or vapor. P1 =  relieving pressure, bar abs(bara). This is the set pressure (barg) + overpressure (barg) + atmospheric pressure (bara) – inlet pressure piping loss (barg) T =  absolute relieving temperature of the gas or vapor at the valve inlet, degree Kelvin (℃ + 273)  W = required relieving capacity, kg/hr V = required relieving capacity, N㎥/hr Z = Compressibility factor.
		A = Minimum required discharge area, ㎟ Kd = Coefficient of discharge.  k = specific heat ratio.  M = Molecular weight of the gas or vapor.  P1 = relieving pressure, bar abs(bara). This is the set pressure (barg) + overpressure (barg) + atmospheric pressure (bara) – inlet pressure piping loss (barg) P2 = Pressure at the valve outlet during flow, bar abs(bara). This is the total back pressure (barg) + atmospheric pressure (bara) T =  absolute relieving temperature of the gas or vapor at the valve inlet, degree Kelvin (℃+ 273)  W = required relieving capacity, kg/hr V = required relieving capacity, N㎥/hr Z = Compressibility factor.

 

 

2. USCS units (United States Customary System)

	set pressures ≥ 15 psig	set pressures < 15 psig or Vacuum conditions
Weight flow (lb/hr)
Volumetric flow (scfm)
where	A  = Minimum required discharge area, in^2 C =  Gas constant based upon the ratio of specific heats of the gas or vapor at standard conditions. (use C = 315 if ratio of specific heats is unknown) K = Coefficient of discharge.  Kb = Back pressure correction factor for gas.  Kc = Combination factor for installations with a rupture disc upstream of the valve. (use a 0.9 value for any rupture disc/pressure relief valve combination not listed, and use a 1.0 value when a rupture disc is not installed) M= Molecular weight of the gas or vapor. P1 =  Relieving pressure, psia. This is the set pressure (psig) + overpressure (psig) + atmospheric pressure (psia) – inlet pressure piping loss (psig) T =  Absolute relieving temperature of the gas or vapor at the valve inlet, degree Rankine (℉+ 460)  W = required relieving capacity, lb/hr V = required relieving capacity, scfm Z = Compressibility factor.
		A = Minimum required discharge area, in^2 Kd = Coefficient of discharge.  k = specific heat ratio.  M = Molecular weight of the gas or vapor.  P1 =  Relieving pressure, psia. This is the set pressure (psig) + overpressure (psig) + atmospheric pressure (psia) – inlet pressure piping loss (psig) P2 = Pressure at the valve outlet during flow, psia. This is the total back pressure (psig) + atmospheric pressure (psia) T =  Absolute relieving temperature of the gas or vapor at the valve inlet, degree Rankine (℉+ 460) W = required relieving capacity, lb/hr V = required relieving capacity, scfm Z = Compressibility factor.

 

 

Gas constant, C

상기 계산식에서 사용하는 기체 상수(Gas constant, C)는 표준 조건에서 기체 또는 증기의 비열비에 따르고 각 units에 따라 다른 식을 적용한다.

1. Metric units

다음 식 또는 표를 이용하여 계산한다.

 

<Table 1> Gas constant Values(Metric units)

 

 

2. USCS units (United States Customary System)

다음 식 또는 표를 이용하여 계산한다.

 

<Table 2> Gas constant Values(USCS units)

 

Reference : EMERSON, Pressure relief valve engineering handbook