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Modelling and optimal operation of a natural gas fired natural draft heater
Anton A. Kiss, Edwin Zondervan, Richard Lakerveld, Leyla Özkan (Eds.) Proceedings of the 29th European Symposium on Computer Aided Process Engineering June 16th to 19th, 2019, Eindhoven, The Netherlands. © 2019 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/B978-0-12-818634-3.50165-X
Modelling and optimal operation of a natural gas fired natural draft heater Richard Yentumia,b, Bogdan Dorneanub, Harvey Arellano-Garcia*b,c a
Department of Engineering & Maintenance, Ghana National Gas Company, Accra, Ghana b
Department of Chemical & Process Engineering, University of Surrey, Guildford, United Kingdom c
LS Prozess- und Anlagentechnik, Brandenburgische Technische Universität CottbusSenftenberg, Cottbus, Germany [email protected]
Abstract Current industrial trends promote reduction of material and energy consumption of fossil fuel burning, and energy-intensive process equipment. It is estimated that approximately 75% of the energy consumption in hydrocarbon processing facilities is used by such equipment as fired heater, hence even small improvements in the energy conservation may lead to significant savings [1, 2]. In this work, a mathematical modelling and optimisation study is undertaken using gPROMS® ProcessBuilder® to determine the optimal operating conditions of an existing API 560 Type-E vertical-cylindrical type natural draft fired heater, in operation at the Atuabo Gas Processing Plant (GPP), in the Western Region of Ghana. It is demonstrated that the optimisation results in significant reduction of fuel gas consumption and operational costs. Keywords: fired heater, tubular heater, mathematical modelling, optimisation, gPROMS.
1. Introduction Fired heaters, also commonly called furnaces, are a primary source of thermal energy for process heating operations in petroleum refining and chemical plants. They have been studied extensively, both experimentally and theoretically, and previous work [1-3] draws attention to the need of conserve energy, improve energy efficiency and reduce carbon emissions. Notably, most fired heaters models from literature are lumped parameter models with steady-state assumptions, mainly due to the complex thermodynamic mechanisms making the problem computationally expensive to solve [1-3]. For instance, longitudinal and radial variations or temperature gradients of the hot flue gases along the vertical height of the fired heater are normally ignored. The novel approach adopted for this work involves the distributed parameter system modelling of the temperature profiles in the tubular coils and the heat transfer fluid (HTF). The resulting ‘white-box’ model may serve as basis for conducting simulation studies to aid decision-making and to identify the best operating conditions within the specified constraints that minimise the operational costs. The model is applied to a 15.8 MW fired heater (H600) in operation at the GPP. The total heat input is supplied by the combustion reaction of fuel gas and combustion air occurring in 8 sets of floor mounted, upwards firing, gas only pre-mix
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main burners. A fuel gas-fired pilot is also supplied to each set of main burners. Aside the need to improve efficiency, significant deviations from the desired HTF supply temperature have on many occasions hampered smooth operation. Currently, there is no validated model of H600 to aid monitoring of thermal efficiency, to identify areas for process improvements and to aid trouble-shooting of process deviations. Furthermore, the current temperature control scheme has been ineffective at rejecting disturbances such as changes in fuel gas pressure.
2. Mathematical model The mathematical model is applied for each section of H600 (Fig.1), namely convection (CS), shield (SS) and radiant section (RS). A 1D tube coil running through the RS, SS and CS is considered. The axial variation is related to the tube wall and the HTF temperatures, while the flue gas temperature along the sectionalised vertical height of the heater is lumped. The tubes in the SS are assumed isolated from the RS. All tube coils are uniformly heated. The combustion process is assumed to be steady-flow and the CO2, N2 and other non-hydrocarbon components of the fuel are ignored in combustion reaction calculations. Key geometrical characteristics of H600 are summarised in Table1. Fig.1: The distinct sections in a box-type style fired heater
Table1: Geometry of the fired heater Parameter
Radiant section
Shield section
Convection section
Number of tubes
88
24
72
Overall length [m]
138.69
21.8
62.94
Outside tube diameter [mm]
114.3
114.3
114.3
Effective tube length [m]
12.192
6.245
6.245
217.8
33.27
-
Total heating area (bare) [m ]
398.46
53.86
-
Total heating area [m2]
-
-
1946
Orientation of tubes
Vertical
Horizontal
Horizontal
Tube material of construction
ASTM A106 Gr.B
ASTM A106 Gr.B
ASTM A106 Gr.B
2
Cold plane surface area [m ] 2
2.1. Radiant section/firebox On a rate basis, the conservation of energy in the fired heater is given by: ܳி ܳ ൌ ܳோ ܳௐ ܳீ
(1)
Where QF=the total rate of heat released by the combustion of the fuel gas [W]; Qair=the rate of heat flow into the burners in the combustion of air [W]; QR=the heat duty of the RS [W]; QWL=total rate of heat loss through the fired heater walls [W]; QG=rate of heat flow out of the RS in the flue gases [W]. ሶಷషಾಳ ȉுಷ
ܳி ൌ ܰ ȉ ቆ݉݅݊ ቀߟெ ȉ ቀ
ேಳ
ቁ ǡ ܳெ௫ுோିெ ቁ ݉݅݊ ቀߟ ȉ ቀ
ሶಷషುಳ ȉுಷ ேಳ
ቁ ǡ ܳெ௫ுோି ቁቇ
(2)
987
Modelling and optimal operation of a natural gas fired natural draft heater
With NB=number of burner in use; ȘMB, ȘPB=efficiency of the main/pilot burners; LHVF=lower heating value of the fuel gas [J/kg]; QMaxHR-MB, QMaxHR-PB=design maximum rate of heat released per main/pilot burner [W]; ۦF-MB, ۦF-PB=total mass flowrate of fuel gas supplied to main/pilot burners [kg/s]. Based on the ratios of the maximum heat released per pilot burner to the main burner, ۦF-PB is assumed to be 0.0133% of ۦF-MB. ܳ ൌ ݉ሶ ܽܿݐെܽ݅ ݎȉ ܿܽ݅ ݎȉ ൫ܶܽ݅ ݎെ ܶ ݂݁ݎ൯
(3)
Where ۦact-air=actual mass flowrate of air supplied to burners [kg/s]; cair=mass specific heat capacity of air [J/kgK]; Tref=reference temperature [K]; Tair=temperature of air [K]. ସ ସ ܳோ ൌ ܨȉ ߪ ȉ ߙ ȉ ܣǡ ȉ ൫ܶீ െ ܶ௪ǡ௩ǡ ൯ ݄ீ ȉ ܣௌ ȉ ൫ܶீ െ ܶ௪ǡ௩ǡ ൯
(4)
With F=overall heat exchange factor to allow for both geometry and non-blackbody emissivities of cold and hot bodies; ߪ=the Stefan-Boltzmann constant [W/m2K4]; Acp,r=area of cold plane replacing a bank of RS tubes [m2]; AS,r=total outside area of the RS tubes [m2]; hGr=convection heat transfer coefficient flue gas-outside of the tube wall [W/m2K]; TGr=temperature of flue gases leaving RS [K]; Tw,avg,r=average temperature of the wall in the RS, calculated as the mean between the temperature at the entrance and the temperature at the exit of the section [K]. ܳௐ ൌ ݂ௐ ȉ ܳ
(5)
With fWL=factor of fired heater wall losses; Qin=total rate of heat into the fired heater [W]. The overall enthalpy of the flue gases is expressed as the sum of the product of the molar flow rates and the specific heat capacities of each component gas. Thus: ܳீ ൌ σ ݊݅ ȉ ߂݉ܪǡ݅
(6)
With ni=molar flowrate of component i released by the combustion reaction [kmole/s]; ߂ܪǡ =the molar enthalpy change of component i [J/kmole]. The rate of change and axial variation of the thermal energy per unit length of tube wall and the HTF are given as: డுೢೝ ሺ௧ǡ௭ሻ డ௧
ସ ସ ሺݐǡ ݖሻ൯ ݄ீ ȉ ߨ ȉ ܦ ȉ ൫ܶீ െ ܶ௪ ሺݐǡ ݖሻ൯ െ ݄ ȉ ߨ ȉ ܦ ȉ ൫ܶ௪ ሺݐǡ ݖሻ െ ൌ ܨȉ ߪ ȉ ߨ ȉ ܦ ȉ ൫ܶீ െ ܶ௪
ܶ ሺݖǡ ݐሻ൯
(7) ߨȉʹܦ
డுಽೝ ሺ௧ǡ௭ሻ
ൌ െ ݎܮݑȉ ݅ ȉ ܪ ሺݐǡ ݖሻ ݄ ݎܮȉ ߨ ȉ ݅ܦȉ ൫ܶ ݎݓሺݐǡ ݖሻ െ ܶ ݎܮሺݖǡ ݐሻ൯ (8) డ௧ Ͷ Where HLr=the enthalpy of the wall in the RS; Do, Di=the outer/inner tube diameter [m]; TGre=the effective radiating gas temperature [K]; Twr=temperature of the wall in the RS [K]; hLr=convection heat transfer coefficient wall-HTF [W/m2K]; TLr=temperature of the HTF in the RS [K]. A general balance equation for the combustion of gaseous hydrocarbon fuels with dry excess air is published by [2] in the form:
ܥ ܪ ߝ ቀ ܣ ቁ ሺܱଶ ͵Ǥʹܰଶ ሻ ՜ ܣȉ ܱܥଶ ܪଶ ܱ ሺߝ െ ͳሻ ቀ ܣ ቁ ܱଶ ߝ ቀ ܣ ቁ ͵Ǥʹܰଶ (9) ସ ଶ ସ ସ
Where ߝ = excess air. While the conservation of mass for the flue gases is expressed as: ݉ሶி ݉ሶ ൌ σ ݉ሶ (10). The composition of the fuel gas is assumed as: 65.59% C1; 17.8032% C2; 12.2454C3; 0.8817% i-C4; 1.5703 n-C4; 0.1766% i-C5; 0.1303 n-C5; 0.0515% C6+; 0.0231% N2 and 1.4976% CO2. With ۦF=total mass flowrate of fuel gas [kg/s]; ۦAir=total mass flowrate of air [kg/s]; i=CO2; H2O; O2; N2. The temperature control valve is modelled as in [8]. For the SS and CS, the heat transfer equations are written as: ܳௌ௧ ൌ ܳௌ௧ǡ െ ܳௌ௧ǡ௨௧
(11)
The rates of heat for the flue gases in and out of the sections are calculated using a thirddegree polynomial function for the specific heat in the form: ܥҧ ൌ ߙ ߚܶ ߛܶ ଶ ߜܶ ଷ . For the wall and the HTF, equations like (7) and (8) are used and adapted to the geometries and operating conditions of the CS and SS, respectively.
988
R. Yentumi et al.
For each section of the fired heater, the general form of the initial and boundary conditions for the temperature of the wall, Tw and the fluid, TF are expressed as: ܶǡௌ௧ ሺͲǡ ݖሻ ൌ ܶ௨௧ǡௌ௧ିଵ ; ܶ௪ǡௌ௧ ሺͲǡ ݖሻ ൌ ܶ௪௨௧ǡௌ௧ିଵ ; ܶ௨௧ǡௌ௧ିଵ , ܶ ;ݐ௪ǡௌ௧ ሺݐǡ Ͳሻ ൌ ܶ௪௨௧ǡௌ௧ିଵ , ݐ
ܶǡௌ௧ ሺݐǡ Ͳሻ ൌ (12)
The Berman equation [1] is used to determine the convection heat transfer coefficient, hGs in the CS: hGs=1.1(hCs+hRs). The radiant heat transfer coefficient is not considered for the finned tube bank of the CS. Ǥଶ଼ Ǥ ݄௦ ൌ ൫ͳǤʹ͵ܶǡ௦ ȉ ܩ௫ǡ௦ ൯ȀܦǤସ (13) With ܩ௫ǡ௦ ൌ ݉ሶீ Ȁܣǡ௦ = flue gas max flux [m/s];ܣǡ௦ =the minimum cross-section
flow area [m2]; Tf,s=the film temperature [K]. The film temperature, Tf,s and the radiant heat transfer coefficient, hRs are calculated from: ܶǡ௦ ൌ ͲǤͷ൫ܶ௪ǡ௩ ܶீ ൯ ݄ோ௦ ൌ ͲǤʹͷͷܶீ െ ʹǤͺͶ
(14) (15)
For each section of the heater, the convection heat transfer coefficients for the inside tube wall and the HTF, varying with the axial position, are calculated from the relation: ݄ ሺݖሻ ൌ ܰݑሺݖሻ ȉ ݇ ሺݖሻȀܦ
(16)
While, within the application ranges, the local Nusselt number is calculated from the Gnielinski correlation [5] and the local Darcy friction factor using Petukhov’s correlation [6]. The heat transfer coefficient for the RS, hGr is specified as 11.36 W/m2K as reported by [7]. The thermophysical properties (density, specific heat capacity, thermal conductivity, and kinematic viscosity) of the tube coil material and the HTF, all of which vary with temperature are expressed in polynomial regression forms obtained using curve fitting techniques of the manufacturer’s thermal data. The heat capacity relation of ASTM A106 Grade B as a function of temperature could not be obtained from literature and Type 304 stainless steel was used instead [4]. The different sections, RS, SS, CS of H600 are connected by mass an energy flows at their boundaries (see Figure 2).
Figure 2: Connectivity between the distinct zones of the fired heater
The parameters for H600, mostly consisting of geometrical quantities are specified in Table 2.
3. Optimisation Energy consumption in the fired heater is to be optimised to identify the best process operating conditions within the specified constraint that minimise fired heater operational costs. The objective function is formulated as an economic model describing the sum of two key daily operating costs: the fuel gas burned, and the electrical power consumed in pumping the HTF: ݂ ൌ ሺͺͶͲͲ ȉ ܿி ȉ ݉ሶி ȉ ܸܪܮி ሻ ൬ܿா ȉ
ிಽ ȉఘȉȉுು ଷǤȉଵల ȉఎು ȉఎಾ
൰ ȉ ݐ (17)
989
Modelling and optimal operation of a natural gas fired natural draft heater
ʹͷ ܸܶ ͷ ͳǤͲ ߝ ͳǤͷ ͳ͵Ͳ ܨ ͵ͶͲ ͷʹ͵Ǥͳͷ ܶ௨௧ ͷͶͺǤͳͷ With VT=valve travel [%]; ܨ =total return volumetric flowrate of HTF to fired heater [m3/h]; Tout=HTF supply temperature [K]; ߟ =pump efficiency=0.75; ߟெ =motor efficiency=0.85; cF=fuel cost=Ǥͳͳ ȉ ͳͲିଽ [$/J]; cE=cost of electric power=0.32 [$/kWh]; g=acceleration due to gravity [m/s2]; HP=pump head=51 [m]; tr=pump runtime per day [h]; ߩ=average density of the fluid=735.16 [kg/m3]. The lower heating value of the flue gas, LHVF was considered equal to 46,890 kJ/kg. Subject to
Table 2: Parameters for the sections of the heater. Parameter
Radiant section
Shield section
Convection section
ߪ, [W/m2K4]
ͷǤͲͶ ȉ ͳͲି଼
ͷǤͲͶ ȉ ͳͲି଼
-
Di, [m]
0.1023
0.1023
0.1023
Do, [m]
0.1143
0.1143
-
Equivalent cold plane area, [m2]
217.88
33.27
-
Overall exchange factor, F
0.590
0.559
-
Reference temperature, Tref [K]
298.15
298.15
298.15
ܳெ௫ுோିெ , [W]
1,472,682
-
-
ܳெ௫ுோି , [W]
29,307
-
-
Mass per unit length of radiant tube coil, [kg/m]
16.07
16.07
20.5
4. Results and discussion A plot of HTF temperature versus the axial position and time in the CS, SS, and RS, are illustrated in Figures 3-5, respectively. An overall temperature profile for the HTF is shown in Figure 6.
Figure 3: HTF temperature in the CS
Figure 4: HTF temperature in the
Table 3 shows a summary of the simulation results compared with measured data from the plant. A base case scenario is considered where the daily operating cost is 1,599.81 $/day, based on a flow of fuel gas of 0.632 kg/s, a HTF return volumetric flow rate of 139.5 m3/h, and a total operating number of burners of 8. The optimisation using the model in gPROMS® resulted in an operating cost of $776.18 $/day, which equals to
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R. Yentumi et al.
283,305.70 $/year. Overall, this translates into savings of about $360,625 $/year compared with the base case scenario. In percentage terms, savings of about 51.48% could be achieved.
Figure 5: HTF temperature in the RS
Figure 6: HTF temperature in H600
Table 3: Simulation results at 380 seconds. Parameter
Predicted
Measured
%Error
Valve travel, VT [%]
50
37.45
-33.51
HTF Supply temperature, Tout [K]
505.58
523.95
3.51
Flue gas temperature, TGr [K]
647.19
758.7
14.7
Average radiant tube wall temperature, [K]
511.84
544.47
5.99
Flue gas temperature at exit of CS, [K]
546.13
520.50
-4.92
For a simulation time of 786 seconds, the optimum supply temperature is identified at 548.4 K. These results demonstrate how a model-based process systems approach can be deployed to achieve optimal operation of the fired heater. However, a more comprehensive study, with a validated model must be carried out before optimal operating conditions can be clearly identified.
5. Conclusions The simulation results of the heater model indicate that the distributed parameter dynamic model proposed in this work closely approximates the actual process behaviour under varied operating conditions. Potential for significant annual savings have been identified. Furthermore, a parameter estimation and model validation should be performed to ensure good agreement between the model predictions and the actual behaviour of H600.
References [1]. H.L. Berman, Fired Heaters, Chemical Engineering, 1978; [2]. J. Baukal, E. Charles, John Zink, 2013, Hamworthy Combustion Handbook – Fundamentals, Vol.1, 2nd Edition, Taylor & Francis Group LLC; [3]. G. Ashbutosh, 1997, Optimise fired heater operations to save money, Hydrocarbon Processing; [4]. J.J. Valencia, P.N. Quested, 2008, Thermophysical properties, ASM Handbook, Vol. 15; [5]. V. Gnielinski, 1976, Int. Chem.Eng. 16, 359; [6]. P. Frank, D.P Dewitt, T.L. Bergman, A.S. Lavine, 2007, Introduction to Heat transfer, 5th Edition, John Wiley & Sons; [7]. R.K. Shah, E.C. Subbarao, R.A. Mashelkar, 1988, Heat transfer equipment designAdvanced Study Institute Book, Hemisphere Publishing Corporation; [8]. ISA Standard 75.01.01-2007 (IEC60534-2-1 Mod), 2007, Flow Equations for Sizing Control Valves
Modelling and optimal operation of a natural gas fired natural draft heater Richard Yentumia,b, Bogdan Dorneanub, Harvey Arellano-Garcia*b,c a
Department of Engineering & Maintenance, Ghana National Gas Company, Accra, Ghana b
Department of Chemical & Process Engineering, University of Surrey, Guildford, United Kingdom c
LS Prozess- und Anlagentechnik, Brandenburgische Technische Universität CottbusSenftenberg, Cottbus, Germany [email protected]
Abstract Current industrial trends promote reduction of material and energy consumption of fossil fuel burning, and energy-intensive process equipment. It is estimated that approximately 75% of the energy consumption in hydrocarbon processing facilities is used by such equipment as fired heater, hence even small improvements in the energy conservation may lead to significant savings [1, 2]. In this work, a mathematical modelling and optimisation study is undertaken using gPROMS® ProcessBuilder® to determine the optimal operating conditions of an existing API 560 Type-E vertical-cylindrical type natural draft fired heater, in operation at the Atuabo Gas Processing Plant (GPP), in the Western Region of Ghana. It is demonstrated that the optimisation results in significant reduction of fuel gas consumption and operational costs. Keywords: fired heater, tubular heater, mathematical modelling, optimisation, gPROMS.
1. Introduction Fired heaters, also commonly called furnaces, are a primary source of thermal energy for process heating operations in petroleum refining and chemical plants. They have been studied extensively, both experimentally and theoretically, and previous work [1-3] draws attention to the need of conserve energy, improve energy efficiency and reduce carbon emissions. Notably, most fired heaters models from literature are lumped parameter models with steady-state assumptions, mainly due to the complex thermodynamic mechanisms making the problem computationally expensive to solve [1-3]. For instance, longitudinal and radial variations or temperature gradients of the hot flue gases along the vertical height of the fired heater are normally ignored. The novel approach adopted for this work involves the distributed parameter system modelling of the temperature profiles in the tubular coils and the heat transfer fluid (HTF). The resulting ‘white-box’ model may serve as basis for conducting simulation studies to aid decision-making and to identify the best operating conditions within the specified constraints that minimise the operational costs. The model is applied to a 15.8 MW fired heater (H600) in operation at the GPP. The total heat input is supplied by the combustion reaction of fuel gas and combustion air occurring in 8 sets of floor mounted, upwards firing, gas only pre-mix
986
R. Yentumi et al.
main burners. A fuel gas-fired pilot is also supplied to each set of main burners. Aside the need to improve efficiency, significant deviations from the desired HTF supply temperature have on many occasions hampered smooth operation. Currently, there is no validated model of H600 to aid monitoring of thermal efficiency, to identify areas for process improvements and to aid trouble-shooting of process deviations. Furthermore, the current temperature control scheme has been ineffective at rejecting disturbances such as changes in fuel gas pressure.
2. Mathematical model The mathematical model is applied for each section of H600 (Fig.1), namely convection (CS), shield (SS) and radiant section (RS). A 1D tube coil running through the RS, SS and CS is considered. The axial variation is related to the tube wall and the HTF temperatures, while the flue gas temperature along the sectionalised vertical height of the heater is lumped. The tubes in the SS are assumed isolated from the RS. All tube coils are uniformly heated. The combustion process is assumed to be steady-flow and the CO2, N2 and other non-hydrocarbon components of the fuel are ignored in combustion reaction calculations. Key geometrical characteristics of H600 are summarised in Table1. Fig.1: The distinct sections in a box-type style fired heater
Table1: Geometry of the fired heater Parameter
Radiant section
Shield section
Convection section
Number of tubes
88
24
72
Overall length [m]
138.69
21.8
62.94
Outside tube diameter [mm]
114.3
114.3
114.3
Effective tube length [m]
12.192
6.245
6.245
217.8
33.27
-
Total heating area (bare) [m ]
398.46
53.86
-
Total heating area [m2]
-
-
1946
Orientation of tubes
Vertical
Horizontal
Horizontal
Tube material of construction
ASTM A106 Gr.B
ASTM A106 Gr.B
ASTM A106 Gr.B
2
Cold plane surface area [m ] 2
2.1. Radiant section/firebox On a rate basis, the conservation of energy in the fired heater is given by: ܳி ܳ ൌ ܳோ ܳௐ ܳீ
(1)
Where QF=the total rate of heat released by the combustion of the fuel gas [W]; Qair=the rate of heat flow into the burners in the combustion of air [W]; QR=the heat duty of the RS [W]; QWL=total rate of heat loss through the fired heater walls [W]; QG=rate of heat flow out of the RS in the flue gases [W]. ሶಷషಾಳ ȉுಷ
ܳி ൌ ܰ ȉ ቆ݉݅݊ ቀߟெ ȉ ቀ
ேಳ
ቁ ǡ ܳெ௫ுோିெ ቁ ݉݅݊ ቀߟ ȉ ቀ
ሶಷషುಳ ȉுಷ ேಳ
ቁ ǡ ܳெ௫ுோି ቁቇ
(2)
987
Modelling and optimal operation of a natural gas fired natural draft heater
With NB=number of burner in use; ȘMB, ȘPB=efficiency of the main/pilot burners; LHVF=lower heating value of the fuel gas [J/kg]; QMaxHR-MB, QMaxHR-PB=design maximum rate of heat released per main/pilot burner [W]; ۦF-MB, ۦF-PB=total mass flowrate of fuel gas supplied to main/pilot burners [kg/s]. Based on the ratios of the maximum heat released per pilot burner to the main burner, ۦF-PB is assumed to be 0.0133% of ۦF-MB. ܳ ൌ ݉ሶ ܽܿݐെܽ݅ ݎȉ ܿܽ݅ ݎȉ ൫ܶܽ݅ ݎെ ܶ ݂݁ݎ൯
(3)
Where ۦact-air=actual mass flowrate of air supplied to burners [kg/s]; cair=mass specific heat capacity of air [J/kgK]; Tref=reference temperature [K]; Tair=temperature of air [K]. ସ ସ ܳோ ൌ ܨȉ ߪ ȉ ߙ ȉ ܣǡ ȉ ൫ܶீ െ ܶ௪ǡ௩ǡ ൯ ݄ீ ȉ ܣௌ ȉ ൫ܶீ െ ܶ௪ǡ௩ǡ ൯
(4)
With F=overall heat exchange factor to allow for both geometry and non-blackbody emissivities of cold and hot bodies; ߪ=the Stefan-Boltzmann constant [W/m2K4]; Acp,r=area of cold plane replacing a bank of RS tubes [m2]; AS,r=total outside area of the RS tubes [m2]; hGr=convection heat transfer coefficient flue gas-outside of the tube wall [W/m2K]; TGr=temperature of flue gases leaving RS [K]; Tw,avg,r=average temperature of the wall in the RS, calculated as the mean between the temperature at the entrance and the temperature at the exit of the section [K]. ܳௐ ൌ ݂ௐ ȉ ܳ
(5)
With fWL=factor of fired heater wall losses; Qin=total rate of heat into the fired heater [W]. The overall enthalpy of the flue gases is expressed as the sum of the product of the molar flow rates and the specific heat capacities of each component gas. Thus: ܳீ ൌ σ ݊݅ ȉ ߂݉ܪǡ݅
(6)
With ni=molar flowrate of component i released by the combustion reaction [kmole/s]; ߂ܪǡ =the molar enthalpy change of component i [J/kmole]. The rate of change and axial variation of the thermal energy per unit length of tube wall and the HTF are given as: డுೢೝ ሺ௧ǡ௭ሻ డ௧
ସ ସ ሺݐǡ ݖሻ൯ ݄ீ ȉ ߨ ȉ ܦ ȉ ൫ܶீ െ ܶ௪ ሺݐǡ ݖሻ൯ െ ݄ ȉ ߨ ȉ ܦ ȉ ൫ܶ௪ ሺݐǡ ݖሻ െ ൌ ܨȉ ߪ ȉ ߨ ȉ ܦ ȉ ൫ܶீ െ ܶ௪
ܶ ሺݖǡ ݐሻ൯
(7) ߨȉʹܦ
డுಽೝ ሺ௧ǡ௭ሻ
ൌ െ ݎܮݑȉ ݅ ȉ ܪ ሺݐǡ ݖሻ ݄ ݎܮȉ ߨ ȉ ݅ܦȉ ൫ܶ ݎݓሺݐǡ ݖሻ െ ܶ ݎܮሺݖǡ ݐሻ൯ (8) డ௧ Ͷ Where HLr=the enthalpy of the wall in the RS; Do, Di=the outer/inner tube diameter [m]; TGre=the effective radiating gas temperature [K]; Twr=temperature of the wall in the RS [K]; hLr=convection heat transfer coefficient wall-HTF [W/m2K]; TLr=temperature of the HTF in the RS [K]. A general balance equation for the combustion of gaseous hydrocarbon fuels with dry excess air is published by [2] in the form:
ܥ ܪ ߝ ቀ ܣ ቁ ሺܱଶ ͵Ǥʹܰଶ ሻ ՜ ܣȉ ܱܥଶ ܪଶ ܱ ሺߝ െ ͳሻ ቀ ܣ ቁ ܱଶ ߝ ቀ ܣ ቁ ͵Ǥʹܰଶ (9) ସ ଶ ସ ସ
Where ߝ = excess air. While the conservation of mass for the flue gases is expressed as: ݉ሶி ݉ሶ ൌ σ ݉ሶ (10). The composition of the fuel gas is assumed as: 65.59% C1; 17.8032% C2; 12.2454C3; 0.8817% i-C4; 1.5703 n-C4; 0.1766% i-C5; 0.1303 n-C5; 0.0515% C6+; 0.0231% N2 and 1.4976% CO2. With ۦF=total mass flowrate of fuel gas [kg/s]; ۦAir=total mass flowrate of air [kg/s]; i=CO2; H2O; O2; N2. The temperature control valve is modelled as in [8]. For the SS and CS, the heat transfer equations are written as: ܳௌ௧ ൌ ܳௌ௧ǡ െ ܳௌ௧ǡ௨௧
(11)
The rates of heat for the flue gases in and out of the sections are calculated using a thirddegree polynomial function for the specific heat in the form: ܥҧ ൌ ߙ ߚܶ ߛܶ ଶ ߜܶ ଷ . For the wall and the HTF, equations like (7) and (8) are used and adapted to the geometries and operating conditions of the CS and SS, respectively.
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For each section of the fired heater, the general form of the initial and boundary conditions for the temperature of the wall, Tw and the fluid, TF are expressed as: ܶǡௌ௧ ሺͲǡ ݖሻ ൌ ܶ௨௧ǡௌ௧ିଵ ; ܶ௪ǡௌ௧ ሺͲǡ ݖሻ ൌ ܶ௪௨௧ǡௌ௧ିଵ ; ܶ௨௧ǡௌ௧ିଵ , ܶ ;ݐ௪ǡௌ௧ ሺݐǡ Ͳሻ ൌ ܶ௪௨௧ǡௌ௧ିଵ , ݐ
ܶǡௌ௧ ሺݐǡ Ͳሻ ൌ (12)
The Berman equation [1] is used to determine the convection heat transfer coefficient, hGs in the CS: hGs=1.1(hCs+hRs). The radiant heat transfer coefficient is not considered for the finned tube bank of the CS. Ǥଶ଼ Ǥ ݄௦ ൌ ൫ͳǤʹ͵ܶǡ௦ ȉ ܩ௫ǡ௦ ൯ȀܦǤସ (13) With ܩ௫ǡ௦ ൌ ݉ሶீ Ȁܣǡ௦ = flue gas max flux [m/s];ܣǡ௦ =the minimum cross-section
flow area [m2]; Tf,s=the film temperature [K]. The film temperature, Tf,s and the radiant heat transfer coefficient, hRs are calculated from: ܶǡ௦ ൌ ͲǤͷ൫ܶ௪ǡ௩ ܶீ ൯ ݄ோ௦ ൌ ͲǤʹͷͷܶீ െ ʹǤͺͶ
(14) (15)
For each section of the heater, the convection heat transfer coefficients for the inside tube wall and the HTF, varying with the axial position, are calculated from the relation: ݄ ሺݖሻ ൌ ܰݑሺݖሻ ȉ ݇ ሺݖሻȀܦ
(16)
While, within the application ranges, the local Nusselt number is calculated from the Gnielinski correlation [5] and the local Darcy friction factor using Petukhov’s correlation [6]. The heat transfer coefficient for the RS, hGr is specified as 11.36 W/m2K as reported by [7]. The thermophysical properties (density, specific heat capacity, thermal conductivity, and kinematic viscosity) of the tube coil material and the HTF, all of which vary with temperature are expressed in polynomial regression forms obtained using curve fitting techniques of the manufacturer’s thermal data. The heat capacity relation of ASTM A106 Grade B as a function of temperature could not be obtained from literature and Type 304 stainless steel was used instead [4]. The different sections, RS, SS, CS of H600 are connected by mass an energy flows at their boundaries (see Figure 2).
Figure 2: Connectivity between the distinct zones of the fired heater
The parameters for H600, mostly consisting of geometrical quantities are specified in Table 2.
3. Optimisation Energy consumption in the fired heater is to be optimised to identify the best process operating conditions within the specified constraint that minimise fired heater operational costs. The objective function is formulated as an economic model describing the sum of two key daily operating costs: the fuel gas burned, and the electrical power consumed in pumping the HTF: ݂ ൌ ሺͺͶͲͲ ȉ ܿி ȉ ݉ሶி ȉ ܸܪܮி ሻ ൬ܿா ȉ
ிಽ ȉఘȉȉுು ଷǤȉଵల ȉఎು ȉఎಾ
൰ ȉ ݐ (17)
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Modelling and optimal operation of a natural gas fired natural draft heater
ʹͷ ܸܶ ͷ ͳǤͲ ߝ ͳǤͷ ͳ͵Ͳ ܨ ͵ͶͲ ͷʹ͵Ǥͳͷ ܶ௨௧ ͷͶͺǤͳͷ With VT=valve travel [%]; ܨ =total return volumetric flowrate of HTF to fired heater [m3/h]; Tout=HTF supply temperature [K]; ߟ =pump efficiency=0.75; ߟெ =motor efficiency=0.85; cF=fuel cost=Ǥͳͳ ȉ ͳͲିଽ [$/J]; cE=cost of electric power=0.32 [$/kWh]; g=acceleration due to gravity [m/s2]; HP=pump head=51 [m]; tr=pump runtime per day [h]; ߩ=average density of the fluid=735.16 [kg/m3]. The lower heating value of the flue gas, LHVF was considered equal to 46,890 kJ/kg. Subject to
Table 2: Parameters for the sections of the heater. Parameter
Radiant section
Shield section
Convection section
ߪ, [W/m2K4]
ͷǤͲͶ ȉ ͳͲି଼
ͷǤͲͶ ȉ ͳͲି଼
-
Di, [m]
0.1023
0.1023
0.1023
Do, [m]
0.1143
0.1143
-
Equivalent cold plane area, [m2]
217.88
33.27
-
Overall exchange factor, F
0.590
0.559
-
Reference temperature, Tref [K]
298.15
298.15
298.15
ܳெ௫ுோିெ , [W]
1,472,682
-
-
ܳெ௫ுோି , [W]
29,307
-
-
Mass per unit length of radiant tube coil, [kg/m]
16.07
16.07
20.5
4. Results and discussion A plot of HTF temperature versus the axial position and time in the CS, SS, and RS, are illustrated in Figures 3-5, respectively. An overall temperature profile for the HTF is shown in Figure 6.
Figure 3: HTF temperature in the CS
Figure 4: HTF temperature in the
Table 3 shows a summary of the simulation results compared with measured data from the plant. A base case scenario is considered where the daily operating cost is 1,599.81 $/day, based on a flow of fuel gas of 0.632 kg/s, a HTF return volumetric flow rate of 139.5 m3/h, and a total operating number of burners of 8. The optimisation using the model in gPROMS® resulted in an operating cost of $776.18 $/day, which equals to
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283,305.70 $/year. Overall, this translates into savings of about $360,625 $/year compared with the base case scenario. In percentage terms, savings of about 51.48% could be achieved.
Figure 5: HTF temperature in the RS
Figure 6: HTF temperature in H600
Table 3: Simulation results at 380 seconds. Parameter
Predicted
Measured
%Error
Valve travel, VT [%]
50
37.45
-33.51
HTF Supply temperature, Tout [K]
505.58
523.95
3.51
Flue gas temperature, TGr [K]
647.19
758.7
14.7
Average radiant tube wall temperature, [K]
511.84
544.47
5.99
Flue gas temperature at exit of CS, [K]
546.13
520.50
-4.92
For a simulation time of 786 seconds, the optimum supply temperature is identified at 548.4 K. These results demonstrate how a model-based process systems approach can be deployed to achieve optimal operation of the fired heater. However, a more comprehensive study, with a validated model must be carried out before optimal operating conditions can be clearly identified.
5. Conclusions The simulation results of the heater model indicate that the distributed parameter dynamic model proposed in this work closely approximates the actual process behaviour under varied operating conditions. Potential for significant annual savings have been identified. Furthermore, a parameter estimation and model validation should be performed to ensure good agreement between the model predictions and the actual behaviour of H600.
References [1]. H.L. Berman, Fired Heaters, Chemical Engineering, 1978; [2]. J. Baukal, E. Charles, John Zink, 2013, Hamworthy Combustion Handbook – Fundamentals, Vol.1, 2nd Edition, Taylor & Francis Group LLC; [3]. G. Ashbutosh, 1997, Optimise fired heater operations to save money, Hydrocarbon Processing; [4]. J.J. Valencia, P.N. Quested, 2008, Thermophysical properties, ASM Handbook, Vol. 15; [5]. V. Gnielinski, 1976, Int. Chem.Eng. 16, 359; [6]. P. Frank, D.P Dewitt, T.L. Bergman, A.S. Lavine, 2007, Introduction to Heat transfer, 5th Edition, John Wiley & Sons; [7]. R.K. Shah, E.C. Subbarao, R.A. Mashelkar, 1988, Heat transfer equipment designAdvanced Study Institute Book, Hemisphere Publishing Corporation; [8]. ISA Standard 75.01.01-2007 (IEC60534-2-1 Mod), 2007, Flow Equations for Sizing Control Valves