Page 306 - Sustainable On-Site CHP Systems Design, Construction, and Operations

Sustaining Operational Ef ficiency of a CHP System 279

constant value for the heat capacity, c can be evaluated at the average of the HRU
p,ex
inlet and outlet temperatures.
Using Eqs. (17-12) and (17-13), Eq. (17-11) can be rewritten as

ρ ( vc ) (T − T )
ε = p HRU,w HRU, ,w o HRU, ,w i (17-14)
HRU −
ρ ( vc ) (T T )
w
p HHRU,min HRU,ex,i HRU, ,i
Similarly, if hot air is generated instead of hot water, Eq. (17-14) can be rewritten as
ρ ( vc ) (T − T )
ε = p HRU,a HRU, ,a o HRU, ,a i (17-15)
HRU −
ρ ( vc ) (T T )
H
p HRU,min HRU,ex,i HRU, ,i
a
One of the flow rates appearing in Eq. (17-14) can be eliminated using a heat bal-
ance on the HRU, that is, the heat loss by the exhaust gas as it passes through the HRU
(Q ) is equal to the sum of the heat gain by the water as it passes through the HRU
HRU,ex
(Q ) and heat losses through the walls of the HRU (L ):
HRU,w HRU
Q = Q + L (17-16)
HRU,ex HRU,w HRU
Here,
Q = (ρ vc ) T ( − T ) (17-17)
HRU,ex p HRU,ex HRU,ex, i HRU,ex, o
and
Q = (ρ vc ) T ( − T ) (17-18)
HRU, w p HRU, w HRU,, HRU,,
w i
w o
The rate of heat loss through the walls will generally be very small compared to
both Q and Q [approximately 1.5 percent of Q for a heat recovery steam
HRU, ex HRU,w HRU,ex
generator (HRSG) according to Kovacik (1982), p. 213)]. Therefore, L can be neglected
HRU
without introducing significant errors, and v can be obtained as a function of
,
HRU ex
v from Eq. (17-16) as
HRU, w
(ρ c ) T ( − T )
v = p HRU, w HRU, w o , HRU , w i , v (17-19)
HRU,ex (ρ c ) (T − T ) HRU,w
,
p HHRU,ex HRU ex,i HRU ex,o
,
Substituting this expression for v into Eq. (17-14), we obtain
HRU,ex
(T − T )
ε = HRU,ex,i HRU,ex,o (17-20)
HRU (T − T )
HRU,ex,i HRU,w,,i
for an HRU that uses exhaust gases from a prime mover to produce hot water, when
(ρ vc ) = (ρ vc ) , which will ordinarily be true.
p HRU, min p HRU, ex
Following similar logic for an HRU that uses exhaust from a prime mover to heat
air, from Eq. (17-15),
(T − T )
ε = HRU,ex,i HRU,ex,o (17-21)
HRU (T − T )
HRU,ex,i HRU,a,,i