Causal Model for Peak and Off Peak Waste Heat Recovery for Chilled Water Production

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:

The main equation used for calculation of waste heat is given as Abdul Karim and Waden (2011):

(1)

Where, cp_g is the specific heat of exhaust gas, T_ex is the temperature of exhaust gas and is mass flow rate of exhaust heat and is defined in equation (Rahman et al., 2011):

(2)

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.

(3)

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:

(4)

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.

(5)

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

(6)

Goodness of fit values:
SSE: 1.739e+008
R-square: 0.5034

(7)

Goodness of fit values:
SSE: 7.566e+007
R-square: 0.784

(8)

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.