Graphical Prediction of Optimum Pinch Point Value with AEA Software Simulation and Validation Applied in Closed Cycle Gas Power Plant

PA method is developed in last four decades, is particularly used in thermal process to predict the maximum energy saving and hot & cold utility requirement. Thereby, optimum design for HEN can be obtained [1].

Such that energy saving can minimize the operating cost in the process [2] and optimum retrofit for HEN [3]. Applying PA IN the WTPS Wanakbori Gujarat power plant to reach an optimum plant design. Starting with ∆Tmin =25℃, so this leads to enhancing the performance of the plant by 47.19% from the 46.78% and decrease the mass of fluid by 0.19 kg/s, which may lead to enhance the plant performance [4, 5]. Applied PA in naphtha unit to reach to optimum HEN design for the plant with ∆Tmin =16℃, there is no improvement in the cost of the process conducted due to decreasing heat and cold loading [6].

Choosing ∆Tmin value of 10℃ [7], PA resulted in good savings of energy for heat utility and cold utility requirement. However, the retrofit of HEN design is important to reach to optimum design for maximum heat recovery Qrec., lead to decrease in CO₂ emissions from the plant [8].

The fact that selecting any value of ∆Tmin will be subjected to a tradeoff between energy cost and capital cost. Such calculation and with the help of specific chart to arrive at the proper cost-wise results. The composite curve shows graphically the smallest distance between hot composite curve (HCC) and cold composite curve (CCC), where a positive value of ∆Tmin must be assigned, i.e. for ∆Tmin > 0. Qrec. is connected with the value ∆Tmin so heating and cooling utility are also related to the change with ∆Tmin [9].

The design of HEN and the retrofit for it to arrive to better solution for the plant is depending on the value for temperature difference between hot and cold utility [10]. Several published work [11-13] have investigated operating and capital cost with respect to specific value of ∆Tmin in order to improve heat transfer process and thereby arrive at the best HEN design.

The optimum HEN design is subjected to tradeoff between energy and capital cost and the period of lifetime of HEN [14].

In some designs of HEN is with stream splitting and this method gives a good solution for heat transfer in the process [15]. There are methods to reach to optimum design for HEN with differential evolution to identified the heat loads in the HE [16].

All of the above reviewed research applied PA to improve system performance in terms of operating or capital costs.

However, a selective operating condition was almost a common approach for all researches.

Since (∆Tmin) is a key factor in this respect, then our current work is evaluation attempt for optimum (∆Tmin) graphically to identity maximum Qrec. process that minimize QHmin & QCmin requirement and this we believe is economic achievement.

It is clear from the general theoretical and practical work of the above published studies, PA based on the mathematical and graphical approach is almost always arrive at similar conclusion with respect to energy saving. Therefore, the case study attempt in this paper will be applied to closed power cycle with operating conditions similar to that of Al-khairat gas turbine plant to investigate for possible heat recovery (Qrec.) in all cycle thermal process.

In this respect, the optimum (∆Tmin) should be predicted in order to identify the maximum Qrec. process that minimize the QHmin & QCmin requirement using the software simulation for the best HEN design.

At the end of this Introduction, and in order to achieve the above design objectives, the paper project will be conducted according to the following work program:

• 2. THEORETICAL OBJECTIVES.
• 3. MATHEMATICAL MODELLING.
• 4. ACTUAL GRAPHICAL PREDICTION.
• 5. COMPUTER SOFTWARE APPLICATION FOR CLOSED SYSTEM DESIGN.
• 6. RESULTS AND DISCUSSION.
• 7. CONCLUSIONS AND RECOMMENDATIONS.

3.1 Theoretical model

Several assumptions were made prior to the theoretical analysis steps. These are:

1. Air is the cycle working fluid.

2. Fuel mass flow is neglected compared high air mass flow.

3. The same (pressure & temperature) in all stages in the power plant.

The mathematical modelling used in the analysis is based on the following:

Ⅰ- heat load in all plant streams, based on the 1^th law of thermodynamics is "an expression of the conservation of energy principle" [17]:

$Q-W=H$

But W=0 because there is no mechanical work when it calculates heat load, and heat load can be expressed as:

$Q=\dot{m} \times C p \times \Delta T$        (1)

Ⅱ- efficiency calculation for the power plant is:

$\eta=P / Q a d d$       (2)

where, the efficiency "The fraction of the heat input that is converted to network output is a measure of the performance of a heat engine and is called the thermal efficiency" [17].

Ⅲ- Temperature outlet from combustion chamber "1-2 Isentropic compression (in a compressor), 3-4 Isentropic expansion (in a turbine) and P2= P3 and P4= P1" [17]:

$\frac{\text { To.cc }}{\text { To.tr }}=\left(\frac{\text { Po.cc }}{\text { Po.tr }}\right)^{\frac{(k-1)}{k}}$ where (k=1.4)                  (3)

Ⅳ- shifted temperature for all streams with ∆Tmin "to allow for the maximum possible amount of heat exchange within each temperature interval. The only modification needed is to ensure that within any interval, hot streams and cold streams are at least ΔTmin apart. This is done by using shifted temperatures" [1].

for hot stream $=$ Thot $-\Delta T \min / 2$          (4)

for cold stream $=T$ cold $+\Delta$ Tmin $/ 2$       (5)

Ⅴ- equation used to calculate heat load in problem table "each interval will have either a net surplus or net deficit of heat as dictated by enthalpy balance, but never both. Knowing the stream population in each interval" [1]:

$\Delta H=(S i-S i+1) \times\left(\sum C P h o t-\sum\right.$ CPcold $)$       (6)

∑CPhot=summation of specific heat in hot streams(kJ/kg.K).

∑CPcold=summation of specific heat in cold streams(kJ/kg.K).

3.2 Theoretical estimation

Acquisition of thermal data were actually obtained from the plant control facilities and from GE documents illustrated Figure 6:

6.png

Figure 6. Thermal data for (P and T) in the closed cycle

The specific heat (Cp) is temperature dependent variables, while mass flow rate in all stages is constant (391.2kg/s) for closed cycle. Furthermore, heat load calculation was conducted using Eq. (1). These results are illustrated in the Table 2.

Table 2. Results for heat load in power plant

No	stream	Ts (℃)	Tt (℃)	Cp kJ/kg.K	$\dot{m}$ kg/s	CP kW/K	∆ H MW
1	HOT	907	483	1.0884	391.2	425.78	180.5
2	HOT	483	32	1.0053	391.2	393.27	177.4
3	COLD	364	907	1.267	391.2	495.65	269.2
4	COLD	32	364	1.061	391.2	415.06	137.8

Efficiency evaluation for closed system power plant by the use of Eq. (2),

η=P⁄Qadd=90MW/269.2MW(100)=0.3343=33.43%

From the GE documents, the fuel price is (35.85 ID/lit) & its heating value (LHV) is (42447kJ/kg).

Since ( $\eta$=33.43%), and (LHV=42447kJ/kg), then η=P⁄Qf=90MW/(42447) $\times \dot{m} f \Rightarrow \dot{m} f$=6.348kg/s.

But the actual fuel rate from plant data is (6.833kg/s), so percent saving of mass of fuel is:

6.833 - 6.348/6.833=0.0709=7.098%

Every unit in the plant is fuel consumption (27.5 m³/hr) from GE documents.

Cost of fuel per hour=35.85 ID×1000 liter×27.5 m³/hr=985,875 ID/hr.

Saving cost per hour=985,875×0.0709=69898.53 ID/hr.

Annual cost reduction= $\frac{1}{h r} \cdot \frac{24 h r}{\text { day }} \cdot \frac{\text { 30days }}{\text { month }} \cdot \frac{12 \text { month }}{\text { year }}=8640 \mathrm{hr} / \mathrm{yr}$.

Annual cost reduction $\left(\frac{I D}{y r}\right)=69898.53\left(\frac{8640 h r}{y r}\right)=604\left(10^6\right)$.

Drawing the (T-H) after calculating the ∆H in all streams in the power plant, the results is illustrated in the Figure 7.

In this figure is clear there is region between hot and cold CC which represent ∆Tmin, and therefore, PA can apply on the power plant. Now applying system PA for a range of (5, 10, 15, 20 and 25) ℃ as a specific in turn values of ∆Tmin, following the same procedure each time to evaluate QHmin, QCmin, and Qrec.

First consideration therefore, is (5℃) ∆Tmin, and PA is carried out to draw CC& GCC diagrams according to the following procedure [1]:

Ⅰ. Apply Eqns. (4 & 5) to evaluate shifted temperature for all streams in the closed cycle with choosing ∆Tmin to allow for the maximum possible amount of heat exchange within each temperature interval and this method is help us to know the streams who rejected or received heat by enthalpy balance by using Eq. (6) for each stream as illustrated in Table 3.

7.png

Figure 7. Composite curve for closed cycle

Table 3. Shifted temperature for ∆Tmin=5℃

No	stream	Ts (℃)	Tt (℃)	Shifted temp. (℃)	Shifted temp. (℃)
1	HOT	907	483	904.5	480.5
2	HOT	483	32	480.5	29.5
3	COLD	364	907	366.5	909.5
4	COLD	32	364	34.5	366.5

Ⅱ. Apply problem table (temperature intervals) is showing in Figure 8.

8.png

Figure 8. Problem table for closed cycle ∆Tmin= 5℃

Ⅲ. Calculate the ∆H for all streams to specified the surplus and deficit streams in the plant by applying Eq. (6) as illustrated in the Table 4:

Ⅳ. Do the infeasible heat cascade step using data from Table 4, as illustrated in the Figure 9:

9.png

Figure 9. Infeasible heat cascade for ∆Tmin=5℃

Ⅴ. Choosing minimum heat load, in this case is at T=34.5℃ with ∆H=-51008.73 kW. Add this heat load to heat cascade again from hot utility [1].

Ⅵ. Add the value of minimum heat load and start the feasible heat cascade to arrive to temperature where ∆H equal zero. This temperature represents pinch point, as illustrated in the Figure 10:

10.png

Figure 10. Feasible heat cascade for ∆Tmin=5℃

So the results for applying pinch method for ∆Tmin=5℃ is:

11.png

Figure 11. Composite curve for closed system with ∆Tmin=5℃

This analysis procedure is repeated for the other specified temperature (10,15,20 and 25) ℃, and the results is illustrated below in the Table 5.

Table 5. Value of QHmin, QCmin and Qrec. for different ∆Tmin

3.3 Computer program

The computer program used in our work is Aspen Energy Analyzer AEA-Version V11-2019, by but the data obtained from the power plant (T, Cp and inlet & outlet mass flow rates) in all streams in the process is used in this program.

AEA simulation software is applied to the closed cycle system for a range of ∆Tmin (5, 10, 15, 20 and 25) Because the PA method depends to ∆Tmin between hot and cold utility and by this ∆Tmin reach to optimum design for HEN for the process and this ∆Tmin is different and there is no constant value for it, so by choosing different ∆Tmin and make comparison between them to arrive to better ∆Tmin for the process [1].

The results are shown in the (CC) in Figures 13 and 14.

13.png

Figure 13. Thermal data for closed system

The results for AEA simulation software for the range of ∆Tmin between (5, 10, 15, 20 and 25) ℃ is illustrated in the Table 8.

The results for AEA simulation software is showing that there is decrease in Qrec. and increase in QHmin and QCmin with increase ∆Tmin.

Table 8. Qrec., QHmin and QCmin for AEA simulation

14a.png

(a) For ∆Tmin=5℃

14b.png

(b) For ∆Tmin=10℃

14c.png

(c) For ∆Tmin=15℃

14d.png

(d) For ∆Tmin=20℃

14e.png

(e) For ∆Tmin=25℃

Figure 14. CC for closed cycle for (a) ∆Tmin=5℃, (b) ∆Tmin=10℃, (c) ∆Tmin=15℃, (d) ∆Tmin=20℃, (e) ∆Tmin=25℃

Thereafter, system GCC are applied for the same temperature range (5, 10, 15, 20 and 25), and the results are shown in the Figure 15.

15a.png

(a) For ∆Tmin=5℃

15b.png

(b) For ∆Tmin=10℃

15c.png

(c) For ∆Tmin=15℃

15d.png

(d) For ∆Tmin=20℃

15e.png

(e) For ∆Tmin=25℃

Figure 15. GCC for closed system for (a) ∆Tmin=5℃, (b) ∆Tmin=10℃, (c) ∆Tmin=15℃, (d) ∆Tmin=20℃, (e) ∆Tmin=25℃

In this study, the investigation for energy saving in the Al-khairat gas turbine power plant is presented to make assessment for the thermal process in the plant to specified the maximum Qrec. and QHmin & QCmin by applied PA method with closed Brayton cycle with the same operating condition in Al-khairat power plant by applied theoretical calculations and with AEA simulation software.

7.1 Conclusions

By calculating ∆H in all the streams in power plant and applied it firstly in the (T-H) diagram and drawing CC to obtained hot and cold composite curve and finally in the AEA simulation software,

1. Can applied PA method in closed cycle because there is heat transfer area between hot and cold CC.

2. Applied range of ∆Tmin between hot and cold composite curve (5, 10, 15, 20 and 25℃).

3. There are Qrec., QHmin and QCmin for each ∆Tmin in the range.

4. There are more than one design for HEN for each ∆Tmin.

5. Choosing the optimum ∆Tmin for closed cycle by predicted it by drawing the values for Qrec. And QCmin and the optimum ∆Tmin is in the 15℃.

6. The values for Qrec., QHmin and QCmin for design four is respectively for Qrec.=318.330 MW , QHmin=88.607 MW and  QCmin =39.564 MW.

7. The data for the power plant is obtained by actual site- visit and recorded from the control room facilities. Monitoring such values until it reaches steady level to be considered and recorded for paper analysis. In addition, the methodology depends on step by step PA procedure to reach a specific result which predict the chance to apply PA. Otherwise, choosing another temperature difference between hot and cold composite curves. This is time consuming effort, adding to that careful acquisition of data makes considerable limitation to conduct the test program.

7.2 Recommendations

1. In Iraq the gas turbine power plant used is open Brayton cycle, so the recommendation to used closed Brayton cycle for reasons mentioned in this study.

2. For open cycle to benefit from the exhaust gases from turbine by installed heat recovery steam generation.

3. Future research can involve wide range of temperature difference ∆Tmin up to maybe 50℃ Comparison between such results will obviously allow high accuracy for the specified ∆Tmin processes.

Calculation of process operating and capital cost for process and thus comparison between them with temperature difference ∆Tmin will present better opportunity for optimum heat exchanger network design.