INTRODUCTION
Waste heat is produced during energy conversion process. The normal waste heat
temperature produced ranges from 370 to 540°C (UNEP,
2006). This category of waste heat could be utilized to produce chilled
water or hot water. In the case of district cooling plants the steam is used
for operating steam absorption chiller. It is a normal practice the waste heat
recovery from gas turbines as in the district cooling is confined to day time,
i.e., during peak period. While during night time operation, i.e., off peak
period, the waste heat from the gas turbines is not recovered. The waste heat
is emitted to the atmosphere. This is being practiced by Gas District Cooling
(GDC) plant of University Teknologi PETRONAS (UTP) (Gilani
et al., 2006). However, if the off peak waste heat is used to produce
chilled water and the chilled water is stored to thermal energy storage system,
the chilled could then be made available during peak period. This would support
the peak period chilled water requirements as well as provide economic benefits
(Dincer, 2002; Hussain et al.,
2004; Khan et al., 2004).
The objective of this study is to establish a causal model for peak and off
peak waste heat recovery for chilled water production. This would enable the
evaluation of economic feasibility of investment on off peak waste heat recovery
using absorption cooling to produce chilled water which could be used to support
peak period requirements.
Since chilled water is not produced during off peak period it is difficult
to estimate the amount of chilled water that could be produced during off peak
period. Causal relationship was used to address this issue by using mathematical
model which established relationship of peak waste heat and chilled water using
regression. The model was then applied to estimate the amount of chilled water
that can be produced by off peak waste heat.
MATERIALS AND METHODS
Universiti Teknologi PETRONAS Gas District Cooling plant (GDC) plant is a co-generation
plant. The exhaust heat, in this case termed as waste heat, of the gas turbines
is being recovered to produce chilled water. Waste heat recovery using heat
recovery steam generator is only applicable during peak period from 6 am in
the morning to 6 pm in the evening. During off peak operation the waste heat
is not recovered. In order to estimate the potential amount of chilled water
that could be produced during off peak hours the following methodology is used:
| • |
Acquisition and analysis of the gas turbine waste heat produced
during peak and off-peak hours at UTP gas district cooling plant. The peak
was considered as the period from 6 am to 6 pm, while the off peak was taken
from 6 pm to 6 am. The UTP district cooling plant operates two turbines,
each of 5.2 MW at ISO condition |
| |
• |
The amount of waste heat generated in terms of MW was evaluated
at 66.6% which was based on the plant data on May 2009. While the remaining
33.4% is emitted to the environment |
| |
• |
Established a mathematical model between chilled water and waste heat
for the peak period using regression |
| |
• |
The relationship was used to evaluate the amount of chilled water that
can be produced from the waste heat during off peak period |
The main equation used for calculation of waste heat is given as Abdul
Karim and Waden (2011):
Where, cpg is the specific heat of exhaust gas, Tex is
the temperature of exhaust gas and 
is mass flow rate of exhaust heat and is defined in equation (Rahman
et al., 2011):
where, 
is mass flow air and
is the fuel flow rate.
In this study the least square approach is used to develop the model. Three
models are selected for this study namely linear, quadratic and exponential.
Linear model: Equation 3 is the general linear equation
model to relate the chilled water and the waste heat.
where, x representing the independent variable (waste heat) and f(x) representing
the chilled water output, the dependent variable. p1 and p2
are the coefficients of the linear model.
Quadratic model: Quadratic model is a nonlinear model of the basic form
in which the functional part of the model is not linear with respect to the
unknown parameters and the method of least squares is used to estimate the values
of the unknown parameters. The general equation is given by:
Exponential model: Exponentials are often used when the rate of change
of a quantity is proportional to the initial amount of the quantity. It is generally
used to model the data that increases or decreases at a high rate.
where, a and b are coefficients for exponential model. If the coefficient associated
with e is negative, f(x) represents exponential decay. If the coefficient is
positive, f(x) represents exponential growth.
RESULTS
Figure 1 shows the waste heat generated by Turbine A and
Turbine B of the GDC plant, using 66.6% recovery of the total waste heat generated.
This amount was used as the basis for the calculation as it is the practice
at the plant to capture the waste heat for conversion to chilled water. The
remaining 33.4% is emitted to atmosphere.
The total waste heat generated during peak and off peak periods are 85.05 and
52.82 GWh respectively. While the minimum and maximum waste heat generated during
peak period are 6.57 and 9.34 GWh. For the case of off peak waste heat generated,
the minimum and maximum are 4.79 and 5.88 GWh.
Figure 2 and 3 show the amount of waste
heat generated specifically for each turbine, namely Turbine A and Turbine B.
|
| Fig. 1: |
Total waste heat during peak and off peak periods generated
for year 2009 |
|
| Fig. 2: |
Waste heat during peak and off peak periods generated by turbine
A for year 2009 |
|
| Fig. 3: |
Waste heat during peak and off peak periods generated by turbine
B for year 2009 |
The total waste heat generated during peak and off peak periods by Turbine
A are 38.11 and 16.58 GWh respectively. The minimum and maximum waste heat generated
during peak period, are 2.17 and 5.19 GWh. While the minimum and maximum off
peak waste heat generated are 1.08 and 3.45 GWh.
The total waste heat generated during peak and off peak periods by Turbine
B are 46.95 and 36.24 GWh, respectively. The minimum and maximum waste heat
generated during peak period are 3.75 and 5.49 GWh. While the minimum and maximum
off peak waste heat generated are 2.44 and 4.55 GWh.
Linear, quadratic and exponential equations were used to curve fit the data.
Results of the curve fitting for the three models are as shown in Fig.
4-6 with 95% confidence bound for the coefficients. The
values for the coefficients are included in Table 1. The intervals
indicate 95% chance that the new observations are contained within the lower
and upper prediction bounds. The goodness of fit statistics for the models is
included in Table 2.
|
| Fig. 4: |
Linear least square fitting model |
|
| Fig. 5: |
Quadratic least square fitting model |
|
| Fig. 6: |
Exponential least square fitting model |
| Table 1: |
Coefficients and confidence interval for the linear, quadratic
and exponential models |
 |
| Table 2: |
Goodness of fit statistics for the models |
 |
| • |
The liner model is represented by: |
Goodness of fit values:
SSE: 1.739e+008
R-square: 0.5034
| • |
The quadratic model is represented by: |
Goodness of fit values:
SSE: 7.566e+007
R-square: 0.784
| • |
The exponential model is represented by: |
Goodness of fit values:
SSE: 1.7064e+008
R-square: 0.5128
CW: Chilled water
WH: Waste heat
Sum of Squares Due to Error (SSE) measures the total deviation of the response
values from the fit to the response values. A value is small or closer to 0
indicates a better fit. In this case the quadratic fitting is the best fit compared
to linear and exponential.
Since the quadratic model is the best fit, the quadratic model was used to
calculate the amount of chilled water that could be produced from off peak waste
heat. Table 3, 4 and 5
show that the amount of chilled water that was obtained using quadratic model
from the off peak waste heat.
| Table 3: |
The estimated total amount of chilled water that can be produced
from waste heat during off peak period by both turbine A and B |
 |
| Table 4: |
The estimated total amount of chilled water that can be produced
from waste heat during off peak period by turbine A |
 |
| Table 5: |
The estimated total amount of chilled water that can be produced
from waste heat during off peak period by Turbine B |
 |
The assumption used 66.6% waste heat recovery from the total off peak waste
heat generated.
The average monthly amount of chilled water that can be produced from off-peak
waste heat by both the turbine A and turbine B is 520,310 RTh. This is 79.7%
of the chilled water produced during the peak period.
DISCUSSION
The analysis of the waste heat generated by Turbine A and Turbine B indicate
that substantial waste heat was generated by both turbines during peak and off
peak periods during the study period. Using the causal relationship of the peak
waste heat generated with chilled water produced, three models namely linear,
quadratic and exponential were formulated. The models are all having R2
values greater than 0.5. Since the R2 value for the quadratic model
is the highest, the quadratic model was used to estimate the amount of chilled
water that can be produced from the off peak waste heat. The amount of chilled
water that can be produced is 520,310 RTh monthly. Hence it is justified to
further evaluate, in terms of life cycle analysis, the feasibility of investing
absorption cooling and thermal energy storage system, the recovery of the waste
heat generated during off peak period.
CONCLUSION
The current practice of the plant is to emit the waste heat to atmosphere during
off peak period. Study indicates that substantial amount of waste heat is available
during off peak period. This amount could be put to beneficial use by converting
to chilled water. Further study on technical and economic feasibility of recovery
of the off peak waste heat for chilled water using absorption process is recommended.
ACKNOWLEDGMENTS
Authors would like to acknowledge the financial support provided by Ministry
of Science, Technology and Innovation (MOSTI) and UTP for the project.
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