POWER June 2010 - 59

plant efficiency
2. Conceptual description of a
CHP plant for a rational evaluation
of plant efficiency via the
second law of thermodynamics. F
represents the fuel supplied to the combustion
turbine and P is the net power produced
by the combined cycle. The mean effective
temperature (MET) determines the plant's
total thermal energy output, Q, and ST' represents
the hypothetical steam turbine that
uses Q to produce net power P'. C represents
the hypothetical Carnot engine that
produces E, the plant's total thermal exergy
output. The Carnot engine operates between
MET and a defined ambient temperature, To
Source: GE Energy
.
F
3. The rational or second-law efficiency, ε, of a steam turbine as a
function of throttle conditions. The steam turbine is assumed to have an isentropic
efficiency of 85% and discharges to a condenser vacuum of 1.25 psi (about 2.5 inches
of mercury) for a range of inlet steam pressures and temperatures. Source: GE Energy
ST
GT
P
76%
75%
74%
73%
72%
71%
70%
69%
68%
67%
66%
200
MET
Q
ST'
P'
C
E
T0
Obviously, it is practically impossible to
design a Carnot engine. The state-of-the-art
power plant engineering option available to
a designer today is a steam turbine (ST). For
illustrative purposes, consider what is practically
possible with a ST with 85% isentropic
efficiency discharging to a condenser
at a pressure of 2.5 inches of mercury. Using
29.8 million Btu/h of saturated steam at
125 psia, this ST would generate 1,840 kW
of shaft power for a thermal efficiency of
only 21.1%. Though this seems to be a paltry
number, consider that, when compared
to the theoretically possible maximum of
2,710 kW (only from a hypothetical Carnot
engine), the second-law or " rational "
efficiency of the example steam turbine is
21.1%/31.1% = 67.9%. The term " rational "
conveys the underlying concept of using a
reference point that is theoretically possible
instead of using a reference point that is
(even theoretically) impossible.
Define the Calculation Process
The concepts of exergy and rational efficiency
point to a thermodynamically
June 2010 | POWER
consistent and unassailable evaluation of
the efficiency of a fossil-fired CHP plant.
The exact configuration of the power plant
(simple-cycle gas turbine [GT] or CC
power plant, fossil-fired ST power plant,
integrated gasification CC power plant,
or other), the type of fuel burned (natural
gas, coal, or distillate), and the nature of
product streams (such as steam, hot water,
nitrogen, oxygen, or hydrogen) are absolutely
immaterial. The proposed CHP efficiency
can now be expressed as a simple
formulation, in equation [1]:
P=1,200psia
P=600psia
P=300psia
Saturated
P=150psia
P=100psia
300
400
500 600
700
800
Steam temperature (F)
900 1,000 1,100 1,200
A conceptual graphical description of
where P is the net electric power generated
by the prime movers in the plant; F is
the total fuel consumed by the boilers, GT
combustors, and similar combustion equipment
in the plant on a net or gross basis,
that is lower heating value (LHV) or higher
heating value (HHV); and Ei is the exergy
of the individual product streams i, where
there are N of them in the particular plant.
Note that, as explained earlier, Ei
is the
maximum theoretically possible work that
can be generated by a Carnot engine. The
term εi
in equation [1] is the second-law
or rational efficiency of a practical engine
(such as a steam turbine) that can reasonably
be expected to convert theoretical Ei
into actual electric power. Note that [1]
can be rewritten in terms of Qi
by using the
exergy-to-energy ratio β, as shown in this
restatement of [1]:
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the ideas encompassed by [1] is shown in
Figure 2. The CC power plant depicted in
Figure 2 has two real products: electric
power, P, and useful thermal energy, Q.
There are two hypothetical products, which
provide a measure of the quality of useful
thermal energy, Q, via the second law of
thermodynamics: thermal exergy E, which
is the power that can be produced by a hypothetical
and impossible Carnot engine,
and the electric power equivalent of Q, P',
which can be produced by a hypothetical
and possible steam turbine, ST'. Note that
P' and E are related to each other by the rational
(second-law) efficiency of the steam
turbine, ST', ε.
Because the most common cogeneration
product is steam, the discussion below will
focus on that.
Thermal energy and exergy, Q and E,
respectively, are fixed by the pressure and
temperature of the product stream. The exit
or condensing conditions of the steam turbine,
ST', are next selected. Please note that
this is the only instance where an assumption
is required to define the CHP efficiency
given by [1]. An isentropic efficiency of
85% and a condenser vacuum of 1.25 psi
(roughly 2.5 inches of mercury) can adequately
represent today's ST technology.
Using the stated efficiency and condenser
vacuum, ST rational efficiency can be cal59
Rational
efficiency (ε)
http://www.powermag.com
POWER June 2010

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