게시판 > 질답게시판 > 장거리 스팀배관에서의 응축수 발생량 계산

스테파노 Stefano

08-04-15 19:42

(1) 질문에 대한 답을 먼저 드리면 계산방법이 틀렸습니다.
과열수증기에서 열손실 전체를 물의 증발잠열로 나누어 계산해서는 안되는 이유는 과열수증기가 열손실에 의해 과열도가 떨어져 엔탈피 감소가 일어나기는 하지만 포화스팀이 되기전 까지는 응축수는 전혀 생기지 않습니다.

즉, 출구측 스팀이 포화스팀이 아니고 과열스팀인 경우 엔탈피는 줄었지만 응축수 발생은 없습니다. 질문의 예에서 출구조건이 과열스팀이므로 전혀 응축수 발생은 없습니다.

(2) 만일 출구측 스팀이 포화스팀인 경우에는 엔탈피 값을 알면 응축수의 양을 계산할 수 있으나 엔탈피값이 없으면 응축수의 양은 계산 할 수 없습니다.

왜냐하면 포화스팀과 평형에 있는 응축수의 양이 달라지더라도 스팀의 온도는 변함이 없기 때문에 온도만으로는 현재 얼마나 응축수의 양을 알 수 없습니다.

(3) 그러나 포화온도에서 기액 혼합물의 전체 엔탈피를 알면 응축되어 있는 응축수의 양을 아래와 같이 계산할 수 있습니다.

포화응축수(Sat'd Liq)의 엔탈피: h1 kcal/kg 예) h1= 251
기-액 혼합물의 엔탈피: h2 kcal/kg 예) h2 =450
포화증기(Sat'd Vap)의 엔탈피: h3 kcal/kg 예) h3 =668

응축수의 비율, f = (h3-h2)/(h3-h1) 예) f = (h3-h2)/(h3-h1) = (668-450)/(668-251) = 0.523

응축수의 비율에 전체의 유량을 곱하면 응축수의 양이 됩니다.

(4) 과열수증기에서는 응축수는 거의 없고, 일부 응축수가 Carry Over 되는 경우 "Steam Quality" 라는 용어를 사용하여 스팀중에 들어있는 Steam의 비율 (혹은 Condensate 비율)을 알 수 있습니다. Steam Quality는 전체무게중 Steam의 무게를 말하기 때문에 100% Steam Qulity는 응축수가 전혀 들어있지 않은 Steam입니다.

(1) 질문에 대한 답을 먼저 드리면  계산방법이 틀렸습니다.  
과열수증기에서 열손실 전체를 물의 증발잠열로 나누어 계산해서는 안되는 이유는 과열수증기가 열손실에 의해 과열도가 떨어져 엔탈피 감소가 일어나기는 하지만 포화스팀이 되기전 까지는 응축수는 전혀 생기지 않습니다.

즉,  출구측 스팀이 포화스팀이 아니고 과열스팀인 경우 엔탈피는 줄었지만 응축수 발생은 없습니다.   질문의 예에서 출구조건이 과열스팀이므로 전혀 응축수 발생은 없습니다.

(2) 만일 출구측 스팀이 포화스팀인 경우에는 엔탈피 값을 알면 응축수의 양을 계산할 수 있으나 엔탈피값이 없으면 응축수의 양은 계산 할 수 없습니다.

왜냐하면 포화스팀과 평형에 있는 응축수의 양이 달라지더라도 스팀의 온도는 변함이 없기 때문에 온도만으로는 현재 얼마나  응축수의 양을 알 수 없습니다.

(3) 그러나  포화온도에서 기액 혼합물의 전체 엔탈피를 알면 응축되어 있는 응축수의 양을 아래와 같이 계산할 수 있습니다.

포화응축수(Sat'd Liq)의 엔탈피:           h1  kcal/kg              예)  h1= 251 
기-액 혼합물의        엔탈피:                h2  kcal/kg              예)  h2 =450
포화증기(Sat'd Vap)의 엔탈피:            h3   kcal/kg             예)  h3 =668

응축수의 비율, f =  (h3-h2)/(h3-h1)    예)  f = (h3-h2)/(h3-h1) = (668-450)/(668-251) = 0.523

응축수의 비율에 전체의 유량을 곱하면 응축수의 양이 됩니다.

(4) 과열수증기에서는 응축수는 거의 없고, 일부 응축수가 Carry Over 되는 경우 "Steam Quality" 라는 용어를 사용하여 스팀중에 들어있는 Steam의 비율 (혹은 Condensate 비율)을 알 수 있습니다.   Steam Quality는 전체무게중 Steam의 무게를 말하기 때문에  100% Steam Qulity는 응축수가 전혀 들어있지 않은 Steam입니다.

별별이야기 Yabrong

08-04-16 08:47

응축수 발생이 없으면 안되는데..

저희 공장에서 다른 공장으로 스팀을 이송할 때 중간에 스팀트랩이 많습니다. 실제로 온도하락이 심한 장거리
배관에 있는 스팀트랩에 호스를 연결해서 드럼통을 놓고 위에 잘 틀어막은 후에 응축수를 받아보니 이와 같은
경우 실제로도 응축수량이 수 t/h에 해당되는 뜨거운 물이 받아졌습니다.

스팀트랩 전문회사에서 주는 식으로 Radiation Loss에 의해 발생하는 응축수량과 비교해 보기 위한 방법으로
해본 계산인데 스테파노님 말씀처럼 열손실 전체를 응축수의 증발잠열로 나누는 부분은 제가 보기에도 이상해
보이는 부분입니다.

제 개념은 point1에서 point2로 갈때 만일 압력하락만 있고 열손실이 없었다면 등엔트로피 변화가
발생해서

point1 point2
p 41 kgf/cm2g 40.5 kgf/cm2g
t 365 degC 364.6 degC
h 747.55 kcal/kg 747.55 kcal/kg

364.4 degC의 온도정도에 있을 것인데 실제로는 열손실이 있어서

p2 = 40.5 kgf/cm2g
t2 = 260 degc
h2 = 677.15 kcal/kg

으로 존재하고 있다고 볼 수 있다는 것으로 이때 f2 유량은 열손실이 응축수 발생으로 유량손실로 이어져
100 t/h보는 것입니다.

100 t/h 40.5 kgf/cm2g 364.6 degC 스팀 = x t/h 40.5 kgf/cm2g 260 degC + (100-x) t/h 응축수
로 볼 수 있다고 생각했습니다.

그런데 여기에서 발란스가 맞게 계산이 아예 안됩니다.
과연 스팀트랩 저문회사에서 준 식으로만 계산해야 하는지 궁금합니다.

스테파노 Stefano

08-04-16 12:09

(1) 열손실량을 알면 이를 (잠열이 아니고) (과열수증기와 출구측 온도에서의 응축수간의 엔탈피차)로 나누면 x를 계산해 낼 수 있겠지요.

응축수량, x = 열손실량/(과열수증기엔탈피-응축수의 엔탈피).................(0)

(2) 열손실량을 모르면 다음과 같이 계산되는데..

열수지: 총엔탈피, 100 t/h @41 KG 365C 스팀 = 총엔탈피, (100-x)t/h @40.5 KG 260C + 열손실, 100 t/h당, Q......(1)
위로부터 손실되는 열량Q와 x의 관계식으로 나타내고 (미지수가 2개라서 이식 만으로 풀수 없으므로)

H1 = H2 + Q ...............................(1a)
100*h1= (100-x)*h2 + Q...............(1b)

100 t/h당 응축수의 양과 응축수가 모두 내놓은(열손실된) 현열과 잠열의 관계식(응축수의 온도는 260도라고 간주)
손실된 열량 = 응축수만큼의 (현열 손실 + 잠열 손실)
Q = x (h1-h3) ......................................................(2)

여기서 h1=747.55 kcal/kg, h2=677.15 kcal/kg, h3= 271.08 kcal/kg (260C Condensate)

(2) 위의 두개의 방정식 (1b)와 (2)로부터
100*h1= (100-x)*h2 + x (h1-h3)...............(3)..................h는 kcal/kg단위, x는 t/h단위

따라서 이를 x에 대해서 풀면 x = 100*(h1- h2)/(h1-h3-h2) = 100*(747.55-677.15)/(747.55-271.08-677.15)
계산하나마나 x가 음수가 나오기 때문에 출구 조건에서는 응축수가 생길수 없다는 계산입니다.

별별이야기 Yabrong

08-04-17 17:44

네 이해가 됬습니다.
열손실을 응축수로 환산한다는 것은 무리가 있으며 열역학적으로 대기로 스팀을 빼내지 않는 이상
응축수발생은 어렵다는 것이 이해가 됬습니다.
대기로 일부 스팀이 빠지고 대기에 노출되면서 응축되는 개념으로 이해를 해야 겠습니다.

Stefano

08-04-17 18:27

(1) 열손실을 응축수 잠열로 나눈 것이 잘못이며
열손실에 의해 출구 온도가 포화된 상태가 된다고 하면
(열손실)/(입구스팀엔탈피-출구조건 응축수엔탈피)로 나누면 계산할 수 있습니다.

(2) 과열수증기관의 스팀트랩 지관이 있을 때 국부적으로 열손실이 발생하고 포화온도보다 낮게 되어 스팀이 손실될 수도 있을 것이나 이를 정량적으로 해석하기는 어렵습니다.

(3) 이런경우 Steam Trap Maker에서는 어떻게 계산하고 있는지 궁금합니다.

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