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A shortcut procedure for calculation of process side heat duty of refinery fired heaters
Accepted Manuscript Title: A Shortcut Procedure for Calculation of Process Side Heat Duty of Refinery Fired Heaters Author: Constantinos Plellis-Tsaltakis PII: DOI: Reference:
S0263-8762(17)30321-0 http://dx.doi.org/doi:10.1016/j.cherd.2017.06.002 CHERD 2704
To appear in: Received date: Revised date: Accepted date:
23-12-2016 2-6-2017 5-6-2017
Please cite this article as: Plellis-Tsaltakis, Constantinos, A Shortcut Procedure for Calculation of Process Side Heat Duty of Refinery Fired Heaters.Chemical Engineering Research and Design http://dx.doi.org/10.1016/j.cherd.2017.06.002 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
A Shortcut Procedure for Calculation of Process Side Heat Duty of Refinery Fired Heaters
Constantinos Plellis – Tsaltakis *
* Corresponding author, Chemical Engineer Ph.D., M.B.A., Green Industrial Technologies, 18 Glafkonos str., Athens 11632, Greece. E-mail address: [email protected], Tel. +30 6977272843, Fax: +30 211 268 6912
Graphical abstract
Highlights Fired heater absorbed duty calculation requires rigorous vapour – liquid equilibrium calculations. Usually costly process simulation software is used. Shortcut procedure is proposed, suitable for implementation in a worksheet. 1
The accuracy of the proposed method is comparable to that of process simulators or to the indirect method. Method may be used on regular basis to reliably monitor fired heater efficiency.
Abstract Absorbed heat duty of process side of a fired heater often requires rigorous vapour – liquid equilibrium calculations and is usually performed with costly process simulator software. An alternative, shortcut method is proposed, which may be easily and efficiently implemented in a spreadsheet. The results of the proposed procedure were checked against those of a process simulator and against the results of the indirect efficiency calculation method, for three different existing refinery furnaces. The accuracy of the proposed method was found comparable to both the others.
Keywords
Fired Heater, Furnace, Refinery, Process side, Heat duty, Absorbed duty
1. Introduction
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Energy efficiency is of paramount importance for modern refineries, mainly due to the high cost of fuel. Efficient processes also reduce greenhouse gas emissions. Energy audits, metrics and benchmarking are invaluable tools for achieving maximum efficiency. Fired heaters are major energy consumers of a refinery, (Devakottai, 2015). Even small reductions in their efficiency, may lead to dramatic increase in fuel consumption. Two methods are available for the calculation of furnace efficiency, the direct and the indirect method. The indirect method aims to calculate the heat loss of a fired heater, based on air excess measurements in the flue gas and the stack temperature, (Abbi and Shashank, 2009), (ASME, 1974). The direct method compares the released heat duty of fuel’s combustion to the absorbed duty of the heated fluid, (Abbi and Shashank, 2009). Both methods have advantages and disadvantages. Usually, the indirect method is used, because it is less demanding in both data and calculations. However, small errors in the air excess due to instrument deviation or air ingress, may lead to severe efficiency underestimation and wrong operating decisions (Lieberman and Lieberman, 2014). On the other hand, direct efficiency calculation may call for vapor – liquid equilibrium calculations. The rigorous calculations may be performed with a process simulator. However, such software is not always available; it is costly and demands some training from the user.
This paper aims to provide an absorbed duty calculation procedure for use in direct fired heater efficiency estimation. The procedure calls for a series of calculations which can be performed easily in a spreadsheet, without the use of special software.
The following paragraph describes briefly the direct and indirect calculation methods.
2. Theory
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2.1 Furnace Efficiency Calculation Methods
The indirect calculation method considers that the heat losses of a fired heater equal the radiation losses from the walls of the heater to the environment plus the losses to the stack, (Abbi and Shashank, 2009), (ASME, 1974), (Patel, 2005). The radiation losses depend on the outside temperature of the furnace walls and their surface area. Typically they are considered to equal 1.5-3% of the heater’s fired duty, (Arora, 1985).
The stack losses consist of the enthalpy that remains in the flue gases before they are sent to the stack. The hotter the flue gases to the stack, the higher the losses. The temperature of the flue gases have a lower limit, below of which acid gases may condense and corrode the heat transfer equipment. This limit strongly depends on the amount of sulfur in the fuel and usually is between 130 – 170oC, (Devakottai, 2015). The amount of heat lost to the stack increases as the flow of flue gas increases. The mass flow of flue gas equals the amount of fuel burnt plus the combustion air. Therefore, the higher the air excess, the higher the flue gas flow and the heat losses to the stack. Air excess is usually maintained at a practical optimum of 3% vol. O2 in the flue gas, (Devakottai, 2015), which provides enough excess air to achieve complete combustion and in the same time does not lead to excessive heat losses to the stack. The indirect method uses excess O2 measurements in the flue gas and stack temperature to estimate the heat losses.
The direct method on the other hand, calculates the absorbed duty, as the enthalpy change of the process side fluid and compares it to the heating value of the fuel burnt. Usually, this method is more difficult to implement than the indirect one, because it needs accurate measurements of fuel and process side flow rates. Moreover, the calculation of the enthalpy change
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of the process side may be difficult without the use of specific, costly software. However, most modern refineries measure accurately enough both the process and the fuel flows in their fired heaters. They also perform enough lab analysis to allow an adequate characterization of the process side fluid and therefore an accurate estimation of its enthalpy change along the furnace. The present work aims to provide a relatively easy and reliable method for the calculation of the absorbed duty, without resorting to special software solutions.
The absorbed duty is analyzed to its main components, namely heating duty, vaporization duty, superheating duty for steam if superheating coils are present in the convection zone, superheating duty for velocity steam if applicable, superheating duty for hydrogen if applicable (hydrotreater fired heaters mainly). Each component’s contribution is calculated separately. The proposed procedure has been developed with the aim to combine as much as possible ease with accuracy. Therefore, liquid specific heats are not treated as constants, but their variation with temperature and feed composition are taken into account. Gas (steam and hydrogen) isobaric specific heat variation with temperature haw been considered. Hydrocarbon enthalpy of vaporization is estimated by the Riedel equation, (Riedel, 1954), taking into account the composition of the vaporizing stream. Percentage of vaporization is not calculated by complex, trial and error liquid – vapor equilibria, but is instead estimated using the generally available distillation curves of the fired heater’s feed, after adjustment for the pressure under which it takes place.
The following paragraph describes the mathematical equations needed for the absorbed duty calculation of refinery fired heaters.
2.2 Process Side Heat Duty Calculation
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The presented method calculates the process side heat duty of a refinery’s fired heater as the sum of the following duties:
Heating duty of the feed.
Vaporization duty for partial evaporation of feed.
Heating duty for injection steam (velocity steam) superheating.
Heating duty for steam superheating, (in case one or more steam superheating coils exist in convection section).
Heating duty for hydrogen heating, (hydrotreaters)
2.2.1 Heating duty of the feed The calculation of the heating duty of the feed assumes that the feed remains at the liquid state from furnace inlet to furnace outlet temperature. The duty is calculated as:
𝐶𝑂𝑇
𝑄1 = 𝑚 ∫
𝐶𝑑𝑇 (1)
𝐶𝐼𝑇
Where: Q1: The heating duty of the feed, (kW) m: The mass flow rate of the feed, (kg/s) CIT: The furnace inlet temperature, (K) COT: The furnace outlet temperature, (K) C: The specific heat of the feed at liquid state, (J/gK)
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Various correlations for C have been proposed, (Watson and Nelson, 1933), (Lee and Kessler, 1976). For the purposes of this work we have implemented the approach of Watson and Nelson, (1933). The correlation is summarized in equation (2).
𝐶 = 4.1868𝐴1 (𝐴2 + 𝐴3 𝑇) (2) Where: C: The specific heat of the feed at liquid state, (J/gK) A1,A2,A3: Parameters related to feed’s composition, defined by equations (3),(4) and (5).
𝐴1 = 0.055𝐾𝑊 + 0.35 (3) Where: KW: The Watson characterization factor, defined by equation (6) , (unitless)
𝐴2 = 0.6811 − 0.308𝑆𝐺60 (4) Where: SG60: The feed’s specific gravity at 15.6oC (60oF)
𝐴3 = 0.000815 − 0.000306𝑆𝐺60 (5) Where: SG60: The feed’s specific gravity at 15.6oC (60oF)
𝐾𝑊 = 3√1.8𝑇50 /𝑆𝐺60 (6) Where: KW: The Watson characterization factor, (unitless) T50: The normal mean boiling point of the feed, (K) 7
SG60: The feed’s specific gravity at 15.6oC (60oF)
Integrating equation (1), using equation (2), leads to equation (7).
𝑄1 = 2.3263[𝐴1 𝐴2 (1.8𝐶𝑂𝑇 − 459.688) +
𝐴1 𝐴3 (1.8𝐶𝑂𝑇 − 459.688)2 − 𝐴1 𝐴2 (1.8𝐶𝐼𝑇 2
𝐴1 𝐴3 (1.8𝐶𝐼𝑇 − 459.688)2 − 459.688) − ] 2
(7)
Where: Q1: The heating duty of the feed at liquid state, (kJ/kg) A1,A2,A3: Parameters related to feed’s composition, defined by equations (3),(4) and (5). CIT: The furnace inlet temperature, (K) COT: The furnace outlet temperature, (K)
2.2.2 Vaporization duty for partial evaporation of the feed
The calculation of the vaporization duty for partial evaporation of the feed assumes that part of it vaporizes isothermally, at T = COT. The amount of feed vaporization and the molar vaporization duty of the feed are needed to calculate the heat duty.
The calculation of the amount of feed vaporized is usually the result of complex vapor – liquid equilibrium calculations. For the needs of this paper, these calculations are substituted by the feed’s True Boiling Point (TBP) distillation curve. TBP distillation curves are not very common for materials other than crude oil. Other distillation curves are easier to obtain, such as atmospheric distillations as per ASTM D-86 for naphtha, kerosene and gasoil, vacuum distillation as per ASTM D-1160 for vacuum distillates and atmospheric residue and simulated
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distillation methods as per ASTM D-2887 for heavier materials. There are correlations for conversion of one standard distillation curve to another, (Daubert and Danner, 1997), (Edmister and Pollock, 1948), (Riazi, 2005). This paper assumes that either original TBP distillation data or curves derived from other standard distillation methods are available. TBP distillation curves are expressed at an absolute pressure of 100kPa(a). Therefore, in order to calculate the amount of material vaporized at the COT the curve must be calculated at the actual partial pressure of hydrocarbons at operation. The actual operating hydrocarbons partial pressure is calculated using equation (8). 𝑃𝐻/𝐶 = 𝑃
𝑀𝑜𝑙𝐻/𝐶 (8) 𝑀𝑜𝑙𝐻/𝐶 + 𝑀𝑜𝑙𝐼𝑛𝑒𝑟𝑡𝑠
Where: PH/C: The partial pressure of hydrocarbons at furnace’s outlet, at operation, (kPa(a)) P: The absolute pressure of hydrocarbons at furnace’s outlet, at operation, (kPa(a)) MolH/C: The molar flow rate of hydrocarbons, (kmol/h) MolInerts: The molar flow rate of inerts, (steam, H2, H2S etc.), (kmol/h)
The TBP distillation curve points at the PH/C can be calculated using equations (9)-(11), (Maxwell and Bonnell, 1957).
𝑋=
5.994296 − 0.972546 log10 (0.1333𝑃𝐻/𝐶 ) (9) 2663.129 − 95.76 log10 (0.1333𝑃𝐻/𝐶 )
Where: X: Parameter for equation (10) PH/C: The partial pressure of hydrocarbons at furnace’s outlet, at operation, (kPa(a))
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𝑇𝑃𝐻/𝐶 =
748.1𝑋𝑇 (10) 1 + 𝑇(0.3861𝑋 − 0.00051606)
Where: X: Parameter, defined by equation (9) TPH/C: The TBP distillation curve temperature point at the partial pressure of hydrocarbons at furnace’s outlet, at operation, (K) T: The TBP distillation curve temperature point at 100 kPa(a), (K)
𝑓 = 0, 𝑖𝑓 𝑇𝑃𝐻/𝐶 < 366𝐾 𝑓=
𝑇𝑃𝐻/𝐶 − 366 , 𝑖𝑓 𝑇𝑃𝐻/𝐶 < 366𝐾 < 477𝐾 111 𝑓 = 1, 𝑖𝑓 𝑇𝑃𝐻/𝐶 < 366𝐾 (10)
Where: f: Correction parameter, for equation (11) TPH/C: The TBP distillation curve temperature point at the partial pressure of hydrocarbons at furnace’s outlet, at operation, (K)
𝑇𝐶𝑃𝐻/𝐶 = 𝑇𝑃𝐻/𝐶 + 1.389𝑓(𝐾𝑊 − 12)(log10 (0.1333𝑃𝐻/𝐶 ) − 2.8808) (11)
Where: TCPH/C: The TBP distillation curve temperature point at the partial pressure of hydrocarbons at furnace’s outlet, at operation, corrected for the aromaticity of the petroleum fraction, (K) f: Correction parameter, defined by equation (10) KW: The Watson characterization factor, as defined in equation (6) (unitless) PH/C: The partial pressure of hydrocarbons at furnace’s outlet, at operation, (kPa) 10
The amount of feed vaporization may be estimated by linear interpolation within the TBP distillation curve temperature points, at the partial pressure of hydrocarbons at furnace’s outlet, at operation, corrected for the aromaticity of the petroleum fraction, as calculated by equation (11).
Riedel equation is used to estimate the molar vaporization duty of hydrocarbons, (Riedel, 1954).
𝛥𝛨𝑉𝐵 = 1.093𝑅𝑇𝐵
ln(𝑃𝐶 /100) − 1.013 (12) 𝑇𝐵 0.93 − 𝑇 𝐶
Where: ΔΗVB: The molar vaporization duty of the hydrocarbon, at its normal boiling point, (Joule/mol) R: The universal gas constant, (8.314 Joule*mol-1*K-1) TB: The normal boiling point of the hydrocarbon, defined as the temperature of 50% evaporation of the TBP curve, at 100 kPa(a) pressure, (K) PC: The critical pressure of the hydrocarbon, as estimated by equation (13), (kPa(a)) TC: The critical temperature of the hydrocarbon, as estimated by equation (14), (K)
The critical properties of a hydrocarbon fraction may be estimated by the Kesler - Lee equations, (13) and (14), (Kesler and Lee, 1976) from its average normal boiling point and specific gravity. The equations have been modified for use of SI instead of the original imperial units.
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ln 𝑃𝐶 = 17.2019 −
0.0566 4.12164 0.213426 − (0.43632 + + ) 10−3 𝑇𝐵 2 𝑆𝐺60 𝑆𝐺60 𝑆𝐺60
+ (4.75794 +
− (2.4505 +
11.81952 1.5301548 + ) 10−7 𝑇𝐵2 2 𝑆𝐺60 𝑆𝐺60
9.9 −10 3 𝑇𝐵 2 ) 10 𝑆𝐺60
(13)
Where: lnPC: The natural logarithm of critical pressure of the hydrocarbon, (Pa) TB: The normal boiling point of the hydrocarbon, defined as the temperature of 50% evaporation of the TBP curve, at 100kPa(a) pressure, (K) SG60: The average specific gravity of the hydrocarbon at 15oC, as estimated by equation (6) when solved for SG60.
𝑇𝐶 = 189.83 + 450.56𝑆𝐺60 + (0.4244 + 0.1174𝑆𝐺60 )𝑇𝐵 +
(0.1441 − 1.0069𝑆𝐺60 )105 𝑇𝐵
(14)
Where: TC: The critical temperature of the hydrocarbon, (K) TB: The normal boiling point of the hydrocarbon, defined as the temperature of 50% vol. evaporation of the TBP curve, at 100 kPa(a) pressure, (K) SG60: The average specific gravity of the hydrocarbon at 15oC, as estimated by equation (6) when solved for SG60.
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Kesler and Lee (1976), presented also a useful correlation for the mean molecular weight of a hydrocarbon fraction, which will be used in this paper together with equation (8), for the calculation of the partial pressure of the hydrocarbons at the furnace outlet:
𝑀𝑊 = −12272.6 + 9486.4𝑆𝐺60 + (8.37414 − 5.99166𝑆𝐺60 )𝑇𝐵
2 ) + (1 − 0.77084𝑆𝐺60 − 0.02058𝑆𝐺60
(0.7465 −
222.466 7 𝑇𝐵 ) 10 𝑇𝐵
+ (1 − 0.80882𝑆𝐺60
2 ) − 0.02226𝑆𝐺60
(0.32284 −
17.3354 12 𝑇𝐵 ) 10 𝑇𝐵3
(15)
Where: MW: The mean molecular weight of the hydrocarbon, (g/mol). SG60: The average specific gravity of the hydrocarbon at 15oC, as estimated by equation (6) when solved for SG60. TB: The normal boiling point of the hydrocarbon, defined as the temperature of 50% vol. evaporation of the TBP curve, at 100kPa(a) pressure, (K).
Equations (12-14) may be used to calculate the vaporization duty of the hydrocarbon at its normal boiling point. However, since the evaporation of hydrocarbons does not take place at 100kPa(a), the enthalpy of vaporization must be calculated at the operating conditions. For this purpose, Watson correlation (Watson, 1933, 1943) may be used:
𝑇1 0.38 1−𝑇 𝐶 𝛥𝛨𝑉 = 𝛥𝛨𝑉𝐵 ( ) 𝑇𝐵 1−𝑇 𝐶 Where: 13
(16)
ΔΗV: The vaporization duty of the hydrocarbon, at the operating temperature, (Joule/mol) ΔΗVB: The vaporization duty of the hydrocarbon, at its normal boiling point, (Joule/mol) T1: The operating temperature, (K) TB: The normal boiling point of the hydrocarbon, defined as the temperature of 50% vol. evaporation of the TBP curve, at 100kPa(a) pressure, (K)
2.2.3 Heat duty for steam superheating / gas heating
Many fired heaters have one or more steam superheating coils in their convection sections. Moreover, live velocity steam may be injected in the coils of some furnaces. Hydrotreater / hydrocracker furnaces also usually heat hydrogen (or the recycle gas of the unit). Such duties may be calculated by equation (1) if the isobaric specific heat (CP) of each gas is known. For the needs of this paper, Shomate equation, (NIST, 2015), is used for CP.
𝐶𝑃 = 𝐴 + 𝐵𝑡 + 𝐶𝑡 2 + 𝐷𝑡 3 +
𝐸 𝑡2
(17)
Where: Cp: The isobaric specific heat of the gas at temperature T, (J/molK) t: A function of absolute temperature T, t=T/1000, (K) A~E: Constants specific to each gas.
Combining equations (1) and (17), the enthalpy change of gas superheating may be calculated: 𝛥𝛨𝐺𝑆𝐻 = 𝐴(𝑡2 − 𝑡1 ) +
𝐵 2 𝐶 𝐷 1 1 (𝑡2 − 𝑡12 ) + (𝑡23 − 𝑡13 ) + (𝑡24 − 𝑡14 ) − 𝐸( − ) 2 3 4 𝑡2 𝑡1
Where:
14
(18)
ΔΗGSH: The enthalpy change of the gas, heated from T1 to T2, (J/mol) t: A function of absolute temperature T, t=T/1000, (K) A~E: Constants specific to each gas.
Values for the constants A~E are available in the bibliography for a wide range of materials. Tables 1 and 2, (NIST, 2015), (Chase, 1998), may be used for steam and hydrogen.
The next paragraph presents a procedure based on equations (1) - (18) for the calculation of the process side duty of a fired heater.
3. Algorithm
Equations (1) – (18) can be used to calculate the process side (absorbed) duty of a fired heater. The required data are:
Fired heater mass feed rate.
Fired heater velocity steam feed rate (if any).
Fired heater hydrogen feed rate (if any).
Superheater coil steam feed rate (if any).
Feed TBP or other distillation curve.
Feed Specific Gravity at 15.6oC (60oF).
Coil Outlet Temperature and Pressure. In the case of distillation column feed preheat furnaces, the flash zone conditions may be used instead.
Coil inlet temperature. 15
Superheater coil inlet and outlet temperatures, (if any).
Velocity steam inlet temperature (if any).
Hydrogen coil inlet temperature (if any).
The proposed algorithm consists of 18 steps and may be easily used to develop a computer program. The following section describes the steps. The algorithm’s flow chart is depicted in Figure 1. The number on the left of each step in Figure 1 corresponds to the step number in the algorithm description below.
1. If a TBP distillation curve of the feed is available, proceed to step 4. 2. Convert all feed distillation data to TBP distillation curve. The conversion procedures need as input the Watson characterization factor, KW. In case KW is not available, suppose KW = 12. 3. Use the temperature of 50% vol. evaporation of the TBP curve calculated in step #2 as input (T50) for equation (6), to calculate a new value for KW. Return to step #2 and use the new value of KW as input for the calculation of the TBP curve. Repeat steps #2 and 3 until KW is calculated. 4. Calculate the mean molecular weight of the feed, using equation (15). 5. Using the result of step #4, the hydrocarbons feed rate, the coil outlet pressure, the velocity steam feed rate if any and the hydrogen feed rate if any, calculate the partial pressure of the hydrocarbons at the furnace outlet,(PH/C) utilizing equation (8). 6. Use the PH/C calculated in step #5, the KW of either step #1 or step #3 and the TBP curve of the feed at 100 kPa(a), (either from step#1 or #3), to calculate the TBP distillation curve points at the partial pressure of the hydrocarbons, implementing equations (9)-(11).
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7. Use the TBP curve calculated in step #6 and the coil outlet temperature of the furnace, to calculate the %volume of evaporation (%EV), of the liquid hydrocarbon feed at the coil outlet conditions, by linear interpolation within the points of the step #6 TBP curve. 8. The volume average normal boiling point of the fraction of the feed that was evaporated inside the furnace may be calculated from the original TBP curve, (either step #1 or step #2) as the temperature that corresponds to (%EV)/2 volumetric evaporation. Use (%EV) from step #8 to calculate the volume average normal boiling point of the evaporated fraction of the feed, (TEV50). 9. Use KW of either step #1 or step #3 and the TEV50 calculated at step #8 as input for equation (6), in order to calculate the mean specific gravity of the fraction of the feed that was evaporated inside the furnace. Equation (6) must be rearranged for the calculation of SG60. 10. Use the TEV50 of step #8 and SG60 of step #9 with equations (13) and (14) to calculate the critical properties of the fraction of the feed that was evaporated inside the furnace. 11. Use the critical properties calculated in step #10 and the TEV50 of step #8 as input for equation (12), to calculate the vaporization duty of the fraction of the feed that was evaporated, at its normal boiling point. 12. Use equation (16), to calculate the vaporization duty of the fraction of the feed that was evaporated, at the operating temperature. Other input for this step are TEV50 of step #8, (as the normal boiling point of the hydrocarbon), the critical temperature of step #10 and the operating temperature at the coil outlet. 13. Use the specific gravity of the whole feed and the KW of either step #1 or step #3, with equations (3),(4) and (5) to calculate respectively the parameters A1, A2 and A3.
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14. Use the coil inlet temperature, the coil outlet temperature and the parameters A1, A2 and A3 from step #13 to calculate the heating duty of hydrocarbons along the coil, with equation (7). 15. Use equation (18), the steam inlet temperature and the coil outlet temperature to calculate the heating duty of the velocity steam, if any. 16. Use equation (18), the steam inlet temperature and the steam outlet temperature to calculate the heating duty of the steam superheating convection coils, if any. 17. Use equation (18), the hydrogen inlet temperature and the coil outlet temperature to calculate the heating duty for the heating of hydrogen, if applicable. 18. Calculate the total absorbed duty of the furnace from the results of steps #12, 14, 15, 16 and 17 and the respective flow rates.
4. Comparison with other methods
The proposed algorithm has been implemented in a computer program. The program has been used to calculate the absorbed duty of existing refinery fired heaters. The absorbed duty of those furnaces has been also calculated by the indirect method and by a commercial rigorous simulation package, using the Soave – Redlich – Kwong equation of state for flash calculation. Table 3 compares the results of the calculations.
The results show that the proposed algorithm has results comparable to a commercial, rigorous simulator. Moreover, both results are very close to those of the usual indirect method. Ta-
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ble 4 provides the details of the absorbed duty calculation for all 3 cases used in Table 3, per algorithm step. Each line represents the corresponding step’s result.
5. Conclusions and Recommendations.
An algorithm for the calculation of the absorbed, (process side) duty of fired heaters was presented. The required data are usual operating and laboratory data (specific gravity and distillation curve of the feed). The proposed method is easy to implement in a usual spreadsheet and in the same time has accuracy comparable to process simulators and to the indirect method. The results of the proposed method are almost identical to those of absorbed duty calculation by process simulator, for the same set of analytical and operational data.
The correlations used in this work, may be substituted with other, more specific if it is deemed necessary. API Databook, (Daubert and Danner, 1997) correlations for critical properties may be used instead of Kesler – Lee, (Kesler and Lee, 1976) equations, or NASA multi parameter isobaric specific heat correlations instead of Shomate polynomials.
As is the general case of direct method, the absorbed duty calculation is sensitive to errors in flow rate measurement. However, modern refineries use adequate instrumentation and usually are able to provide accurate enough measurements. On the other hand, daily laboratory feed analysis needed for process side characterization, are usually more accurate than field flue gas O2 measurements. Moreover, simultaneous use of direct and indirect method may indicate excessive tramp air ingress and thus aid to equipment efficiency improvement.
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References Arora V.K. Check Fired Heater Performance. Hydrocarbon Processing May 1985; 85-7. Abbi Y.P., Shashank J. Handbook on Energy Audit and Environment Management. New Delhi, India: The Energy and Resources Institute, TERI; 2009. American Society of Mechanical Engineers (ASME) Performance Test Code for Steam Generating Units PTC 4.1”, 1974. Chase Jr. M.W., NIST-JANAF Thermochemical Tables. 4th Edition J. Phys. Chem. Ref. Data, Monograph 9, 1998; 1-1951 Daubert T.E., Danner R.P. API Technical Databook – Petroleum Refining. 6th ed. Washington D.C.: American Petroleum Institute (API); 1997. Devakottai B.S. Energy efficiency in furnaces and boilers. In: Rossiter A.P., Jones B.P. Energy Management and Efficiency for the Process Industries. Hoboken: Wiley; 2015. p. 107-27. Edmister W.C., Pollock D.H. Phase Relations for Petroleum Fractions. Chem. Eng. Progr. 1948; vol. 44: 905-26. Ganapathy V. Applied Heat Transfer. 1st ed. Tulsa, Oklahoma: Pennwell Publishing Co.; 1982. Kesler M.G., Lee B. I. Improve prediction of enthalpy of fractions. Hydrocarbon Processing, March 1976; 153 – 8. Lieberman N.P., Lieberman E.T. A Working Guide to Process Equipment. 4th ed. New York: McGraw-Hill; 2014. Linstrom P.J., Mallard W.G., Eds. NIST Chemistry WebBook NIST Standard Reference Database Number 69. National Institute of Standards and Technology, Gaithersburg MD, 20899, http://webbook.nist.gov, (retrieved July 15, 2015). Maxwell J.B., Bonnell L.S. Derivation and Precision of a New Vapor Pressure Correlation for Petroleum Hydrocarbons. Industrial and Engineering Chemistry 1957; 49: 1187- 96. Patel S. Simplify Your Thermal Efficiency Calculation. Hydrocarbon Processing, July 2005; 63-9. Riazi M.R. Characterization and Properties of Petroleum Fractions, American Society for Testing and Materials, 2005. Riedel L. Kritischer Koeffizient, Dichte des gesättigten Dampfes und Verdampfungswärme. Untersuchungen über eine Erweiterung des Theorems der übereinstimmenden Zustände. Teil III. Chemie Ingenieur Technik 1954; 26: 679–83. Trambouze P. Petroleum Refining, Materials and Equipment. 1st ed. Paris: Editions Technip; 2000. 21
Watson K.M., Nelson E.F. Improved Methods for Approximating Critical and Thermal Properties of Petroleum Fractions. Ind. Eng. Chem. 1933; 25 (8): 880–7. Watson K.M. Thermodynamics of the Liquid States, Generalized Prediction of Properties. Ind. Eng. Chem. 1943; 35: 398-406.
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Figure Legends
Figure 1: Algorithm Flow Chart.
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Table 1, Shomate polynomial constants for steam, (NIST, 2015), (Chase, 1998)
Temperature (K) A B C D E F G H
500 - 1700 30.092 6.832514 6.793435 -2.53448 0.082139 -250.881 223.3967 -241.8264
1700 - 6000 41.96426 8.622053 -1.49978 0.098119 -11.15764 -272.1797 219.7809 -241.8264
Table 2, Shomate polynomial constants for hydrogen, (NIST, 2015), (Chase, 1998)
Temperature (K) A B C D E F G H
298 - 1000 33.066178 -11.363417 11.432816 -2.772874 -0.158558 -9.980797 172.707974 0
1000 - 2500 18.563083 12.257357 -2.859786 0.268238 1.97799 -1.147438 156.288133 0
24
Table 3, Absorbed duty as calculated by three different methods
Furnace Type
Indirect
Direct
(pro- Direct (Rig-
(kW)
posed
algo- orous Simu-
Case 1, Vacuum distillation furnace, ca- 34,047
rithm) (kW)
lation) (kW)
34,342
34,265
10,940
10,633
42,644
41,061
thedral type, 2 radiant sections, common convection section, with velocity steam and 2 convection coils for low and medium pressure steam superheating. Case 2, Diesel hydrotreater feed & recycle 10,813 gas, Vertical cylindrical type. Case 3, Vacuum distillation furnace, ca- 42,439 thedral type, 2 radiant sections, common convection section, with velocity steam and 2 convection coils for low and medium pressure steam superheating.
25
Table 4, Details of the absorbed duty calculation for all 3 cases used in Table 3.
Step #
units
1 2 3 4 5 6 7 8 9
unitless g/mol kPa(a) %vol K
10
K ; kPa
11 12
kJ/kg kW
13
unitless
14 15 16 17 18
kW kW kW kW kW
Case 1 No, ASTM D1160 available ok 11.761 562.62 2.753 ok 56% vol 717.6 0.9260 Tc=914.2 K ; Pc=1,123.75 kPa 185.35 11321.3 A1=0.996839; A2=0.385728; A3=0.0005215 28,962.9 323.9 2,036.2 Not applicable 42,644.2
Case 2 No, ASTM D-86 Available ok 11.792 223.08 733.865 ok 37% vol 490.0 0.8133 Tc=730.5 K ; Pc=2,171.39 kPa 233.26 1538.3 A1=0.998533; A2=0.421425; A3=0.000557 8,009.5 Not applicable Not applicable 1,392.0 10,939.8
26
Case 3 No, ASTM D1160 available ok 11.885 644.05 2.642 ok 45% vol 712.0 0.9139 Tc=910.0 K ; Pc=1,099.11 kPa 156.25 5942.8 A1=1.003666; A2=0.384465; A3=0.00052 27,256.0 198.7 944.8 Not applicable 34,342.3
S0263-8762(17)30321-0 http://dx.doi.org/doi:10.1016/j.cherd.2017.06.002 CHERD 2704
To appear in: Received date: Revised date: Accepted date:
23-12-2016 2-6-2017 5-6-2017
Please cite this article as: Plellis-Tsaltakis, Constantinos, A Shortcut Procedure for Calculation of Process Side Heat Duty of Refinery Fired Heaters.Chemical Engineering Research and Design http://dx.doi.org/10.1016/j.cherd.2017.06.002 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
A Shortcut Procedure for Calculation of Process Side Heat Duty of Refinery Fired Heaters
Constantinos Plellis – Tsaltakis *
* Corresponding author, Chemical Engineer Ph.D., M.B.A., Green Industrial Technologies, 18 Glafkonos str., Athens 11632, Greece. E-mail address: [email protected], Tel. +30 6977272843, Fax: +30 211 268 6912
Graphical abstract
Highlights Fired heater absorbed duty calculation requires rigorous vapour – liquid equilibrium calculations. Usually costly process simulation software is used. Shortcut procedure is proposed, suitable for implementation in a worksheet. 1
The accuracy of the proposed method is comparable to that of process simulators or to the indirect method. Method may be used on regular basis to reliably monitor fired heater efficiency.
Abstract Absorbed heat duty of process side of a fired heater often requires rigorous vapour – liquid equilibrium calculations and is usually performed with costly process simulator software. An alternative, shortcut method is proposed, which may be easily and efficiently implemented in a spreadsheet. The results of the proposed procedure were checked against those of a process simulator and against the results of the indirect efficiency calculation method, for three different existing refinery furnaces. The accuracy of the proposed method was found comparable to both the others.
Keywords
Fired Heater, Furnace, Refinery, Process side, Heat duty, Absorbed duty
1. Introduction
2
Energy efficiency is of paramount importance for modern refineries, mainly due to the high cost of fuel. Efficient processes also reduce greenhouse gas emissions. Energy audits, metrics and benchmarking are invaluable tools for achieving maximum efficiency. Fired heaters are major energy consumers of a refinery, (Devakottai, 2015). Even small reductions in their efficiency, may lead to dramatic increase in fuel consumption. Two methods are available for the calculation of furnace efficiency, the direct and the indirect method. The indirect method aims to calculate the heat loss of a fired heater, based on air excess measurements in the flue gas and the stack temperature, (Abbi and Shashank, 2009), (ASME, 1974). The direct method compares the released heat duty of fuel’s combustion to the absorbed duty of the heated fluid, (Abbi and Shashank, 2009). Both methods have advantages and disadvantages. Usually, the indirect method is used, because it is less demanding in both data and calculations. However, small errors in the air excess due to instrument deviation or air ingress, may lead to severe efficiency underestimation and wrong operating decisions (Lieberman and Lieberman, 2014). On the other hand, direct efficiency calculation may call for vapor – liquid equilibrium calculations. The rigorous calculations may be performed with a process simulator. However, such software is not always available; it is costly and demands some training from the user.
This paper aims to provide an absorbed duty calculation procedure for use in direct fired heater efficiency estimation. The procedure calls for a series of calculations which can be performed easily in a spreadsheet, without the use of special software.
The following paragraph describes briefly the direct and indirect calculation methods.
2. Theory
3
2.1 Furnace Efficiency Calculation Methods
The indirect calculation method considers that the heat losses of a fired heater equal the radiation losses from the walls of the heater to the environment plus the losses to the stack, (Abbi and Shashank, 2009), (ASME, 1974), (Patel, 2005). The radiation losses depend on the outside temperature of the furnace walls and their surface area. Typically they are considered to equal 1.5-3% of the heater’s fired duty, (Arora, 1985).
The stack losses consist of the enthalpy that remains in the flue gases before they are sent to the stack. The hotter the flue gases to the stack, the higher the losses. The temperature of the flue gases have a lower limit, below of which acid gases may condense and corrode the heat transfer equipment. This limit strongly depends on the amount of sulfur in the fuel and usually is between 130 – 170oC, (Devakottai, 2015). The amount of heat lost to the stack increases as the flow of flue gas increases. The mass flow of flue gas equals the amount of fuel burnt plus the combustion air. Therefore, the higher the air excess, the higher the flue gas flow and the heat losses to the stack. Air excess is usually maintained at a practical optimum of 3% vol. O2 in the flue gas, (Devakottai, 2015), which provides enough excess air to achieve complete combustion and in the same time does not lead to excessive heat losses to the stack. The indirect method uses excess O2 measurements in the flue gas and stack temperature to estimate the heat losses.
The direct method on the other hand, calculates the absorbed duty, as the enthalpy change of the process side fluid and compares it to the heating value of the fuel burnt. Usually, this method is more difficult to implement than the indirect one, because it needs accurate measurements of fuel and process side flow rates. Moreover, the calculation of the enthalpy change
4
of the process side may be difficult without the use of specific, costly software. However, most modern refineries measure accurately enough both the process and the fuel flows in their fired heaters. They also perform enough lab analysis to allow an adequate characterization of the process side fluid and therefore an accurate estimation of its enthalpy change along the furnace. The present work aims to provide a relatively easy and reliable method for the calculation of the absorbed duty, without resorting to special software solutions.
The absorbed duty is analyzed to its main components, namely heating duty, vaporization duty, superheating duty for steam if superheating coils are present in the convection zone, superheating duty for velocity steam if applicable, superheating duty for hydrogen if applicable (hydrotreater fired heaters mainly). Each component’s contribution is calculated separately. The proposed procedure has been developed with the aim to combine as much as possible ease with accuracy. Therefore, liquid specific heats are not treated as constants, but their variation with temperature and feed composition are taken into account. Gas (steam and hydrogen) isobaric specific heat variation with temperature haw been considered. Hydrocarbon enthalpy of vaporization is estimated by the Riedel equation, (Riedel, 1954), taking into account the composition of the vaporizing stream. Percentage of vaporization is not calculated by complex, trial and error liquid – vapor equilibria, but is instead estimated using the generally available distillation curves of the fired heater’s feed, after adjustment for the pressure under which it takes place.
The following paragraph describes the mathematical equations needed for the absorbed duty calculation of refinery fired heaters.
2.2 Process Side Heat Duty Calculation
5
The presented method calculates the process side heat duty of a refinery’s fired heater as the sum of the following duties:
Heating duty of the feed.
Vaporization duty for partial evaporation of feed.
Heating duty for injection steam (velocity steam) superheating.
Heating duty for steam superheating, (in case one or more steam superheating coils exist in convection section).
Heating duty for hydrogen heating, (hydrotreaters)
2.2.1 Heating duty of the feed The calculation of the heating duty of the feed assumes that the feed remains at the liquid state from furnace inlet to furnace outlet temperature. The duty is calculated as:
𝐶𝑂𝑇
𝑄1 = 𝑚 ∫
𝐶𝑑𝑇 (1)
𝐶𝐼𝑇
Where: Q1: The heating duty of the feed, (kW) m: The mass flow rate of the feed, (kg/s) CIT: The furnace inlet temperature, (K) COT: The furnace outlet temperature, (K) C: The specific heat of the feed at liquid state, (J/gK)
6
Various correlations for C have been proposed, (Watson and Nelson, 1933), (Lee and Kessler, 1976). For the purposes of this work we have implemented the approach of Watson and Nelson, (1933). The correlation is summarized in equation (2).
𝐶 = 4.1868𝐴1 (𝐴2 + 𝐴3 𝑇) (2) Where: C: The specific heat of the feed at liquid state, (J/gK) A1,A2,A3: Parameters related to feed’s composition, defined by equations (3),(4) and (5).
𝐴1 = 0.055𝐾𝑊 + 0.35 (3) Where: KW: The Watson characterization factor, defined by equation (6) , (unitless)
𝐴2 = 0.6811 − 0.308𝑆𝐺60 (4) Where: SG60: The feed’s specific gravity at 15.6oC (60oF)
𝐴3 = 0.000815 − 0.000306𝑆𝐺60 (5) Where: SG60: The feed’s specific gravity at 15.6oC (60oF)
𝐾𝑊 = 3√1.8𝑇50 /𝑆𝐺60 (6) Where: KW: The Watson characterization factor, (unitless) T50: The normal mean boiling point of the feed, (K) 7
SG60: The feed’s specific gravity at 15.6oC (60oF)
Integrating equation (1), using equation (2), leads to equation (7).
𝑄1 = 2.3263[𝐴1 𝐴2 (1.8𝐶𝑂𝑇 − 459.688) +
𝐴1 𝐴3 (1.8𝐶𝑂𝑇 − 459.688)2 − 𝐴1 𝐴2 (1.8𝐶𝐼𝑇 2
𝐴1 𝐴3 (1.8𝐶𝐼𝑇 − 459.688)2 − 459.688) − ] 2
(7)
Where: Q1: The heating duty of the feed at liquid state, (kJ/kg) A1,A2,A3: Parameters related to feed’s composition, defined by equations (3),(4) and (5). CIT: The furnace inlet temperature, (K) COT: The furnace outlet temperature, (K)
2.2.2 Vaporization duty for partial evaporation of the feed
The calculation of the vaporization duty for partial evaporation of the feed assumes that part of it vaporizes isothermally, at T = COT. The amount of feed vaporization and the molar vaporization duty of the feed are needed to calculate the heat duty.
The calculation of the amount of feed vaporized is usually the result of complex vapor – liquid equilibrium calculations. For the needs of this paper, these calculations are substituted by the feed’s True Boiling Point (TBP) distillation curve. TBP distillation curves are not very common for materials other than crude oil. Other distillation curves are easier to obtain, such as atmospheric distillations as per ASTM D-86 for naphtha, kerosene and gasoil, vacuum distillation as per ASTM D-1160 for vacuum distillates and atmospheric residue and simulated
8
distillation methods as per ASTM D-2887 for heavier materials. There are correlations for conversion of one standard distillation curve to another, (Daubert and Danner, 1997), (Edmister and Pollock, 1948), (Riazi, 2005). This paper assumes that either original TBP distillation data or curves derived from other standard distillation methods are available. TBP distillation curves are expressed at an absolute pressure of 100kPa(a). Therefore, in order to calculate the amount of material vaporized at the COT the curve must be calculated at the actual partial pressure of hydrocarbons at operation. The actual operating hydrocarbons partial pressure is calculated using equation (8). 𝑃𝐻/𝐶 = 𝑃
𝑀𝑜𝑙𝐻/𝐶 (8) 𝑀𝑜𝑙𝐻/𝐶 + 𝑀𝑜𝑙𝐼𝑛𝑒𝑟𝑡𝑠
Where: PH/C: The partial pressure of hydrocarbons at furnace’s outlet, at operation, (kPa(a)) P: The absolute pressure of hydrocarbons at furnace’s outlet, at operation, (kPa(a)) MolH/C: The molar flow rate of hydrocarbons, (kmol/h) MolInerts: The molar flow rate of inerts, (steam, H2, H2S etc.), (kmol/h)
The TBP distillation curve points at the PH/C can be calculated using equations (9)-(11), (Maxwell and Bonnell, 1957).
𝑋=
5.994296 − 0.972546 log10 (0.1333𝑃𝐻/𝐶 ) (9) 2663.129 − 95.76 log10 (0.1333𝑃𝐻/𝐶 )
Where: X: Parameter for equation (10) PH/C: The partial pressure of hydrocarbons at furnace’s outlet, at operation, (kPa(a))
9
𝑇𝑃𝐻/𝐶 =
748.1𝑋𝑇 (10) 1 + 𝑇(0.3861𝑋 − 0.00051606)
Where: X: Parameter, defined by equation (9) TPH/C: The TBP distillation curve temperature point at the partial pressure of hydrocarbons at furnace’s outlet, at operation, (K) T: The TBP distillation curve temperature point at 100 kPa(a), (K)
𝑓 = 0, 𝑖𝑓 𝑇𝑃𝐻/𝐶 < 366𝐾 𝑓=
𝑇𝑃𝐻/𝐶 − 366 , 𝑖𝑓 𝑇𝑃𝐻/𝐶 < 366𝐾 < 477𝐾 111 𝑓 = 1, 𝑖𝑓 𝑇𝑃𝐻/𝐶 < 366𝐾 (10)
Where: f: Correction parameter, for equation (11) TPH/C: The TBP distillation curve temperature point at the partial pressure of hydrocarbons at furnace’s outlet, at operation, (K)
𝑇𝐶𝑃𝐻/𝐶 = 𝑇𝑃𝐻/𝐶 + 1.389𝑓(𝐾𝑊 − 12)(log10 (0.1333𝑃𝐻/𝐶 ) − 2.8808) (11)
Where: TCPH/C: The TBP distillation curve temperature point at the partial pressure of hydrocarbons at furnace’s outlet, at operation, corrected for the aromaticity of the petroleum fraction, (K) f: Correction parameter, defined by equation (10) KW: The Watson characterization factor, as defined in equation (6) (unitless) PH/C: The partial pressure of hydrocarbons at furnace’s outlet, at operation, (kPa) 10
The amount of feed vaporization may be estimated by linear interpolation within the TBP distillation curve temperature points, at the partial pressure of hydrocarbons at furnace’s outlet, at operation, corrected for the aromaticity of the petroleum fraction, as calculated by equation (11).
Riedel equation is used to estimate the molar vaporization duty of hydrocarbons, (Riedel, 1954).
𝛥𝛨𝑉𝐵 = 1.093𝑅𝑇𝐵
ln(𝑃𝐶 /100) − 1.013 (12) 𝑇𝐵 0.93 − 𝑇 𝐶
Where: ΔΗVB: The molar vaporization duty of the hydrocarbon, at its normal boiling point, (Joule/mol) R: The universal gas constant, (8.314 Joule*mol-1*K-1) TB: The normal boiling point of the hydrocarbon, defined as the temperature of 50% evaporation of the TBP curve, at 100 kPa(a) pressure, (K) PC: The critical pressure of the hydrocarbon, as estimated by equation (13), (kPa(a)) TC: The critical temperature of the hydrocarbon, as estimated by equation (14), (K)
The critical properties of a hydrocarbon fraction may be estimated by the Kesler - Lee equations, (13) and (14), (Kesler and Lee, 1976) from its average normal boiling point and specific gravity. The equations have been modified for use of SI instead of the original imperial units.
11
ln 𝑃𝐶 = 17.2019 −
0.0566 4.12164 0.213426 − (0.43632 + + ) 10−3 𝑇𝐵 2 𝑆𝐺60 𝑆𝐺60 𝑆𝐺60
+ (4.75794 +
− (2.4505 +
11.81952 1.5301548 + ) 10−7 𝑇𝐵2 2 𝑆𝐺60 𝑆𝐺60
9.9 −10 3 𝑇𝐵 2 ) 10 𝑆𝐺60
(13)
Where: lnPC: The natural logarithm of critical pressure of the hydrocarbon, (Pa) TB: The normal boiling point of the hydrocarbon, defined as the temperature of 50% evaporation of the TBP curve, at 100kPa(a) pressure, (K) SG60: The average specific gravity of the hydrocarbon at 15oC, as estimated by equation (6) when solved for SG60.
𝑇𝐶 = 189.83 + 450.56𝑆𝐺60 + (0.4244 + 0.1174𝑆𝐺60 )𝑇𝐵 +
(0.1441 − 1.0069𝑆𝐺60 )105 𝑇𝐵
(14)
Where: TC: The critical temperature of the hydrocarbon, (K) TB: The normal boiling point of the hydrocarbon, defined as the temperature of 50% vol. evaporation of the TBP curve, at 100 kPa(a) pressure, (K) SG60: The average specific gravity of the hydrocarbon at 15oC, as estimated by equation (6) when solved for SG60.
12
Kesler and Lee (1976), presented also a useful correlation for the mean molecular weight of a hydrocarbon fraction, which will be used in this paper together with equation (8), for the calculation of the partial pressure of the hydrocarbons at the furnace outlet:
𝑀𝑊 = −12272.6 + 9486.4𝑆𝐺60 + (8.37414 − 5.99166𝑆𝐺60 )𝑇𝐵
2 ) + (1 − 0.77084𝑆𝐺60 − 0.02058𝑆𝐺60
(0.7465 −
222.466 7 𝑇𝐵 ) 10 𝑇𝐵
+ (1 − 0.80882𝑆𝐺60
2 ) − 0.02226𝑆𝐺60
(0.32284 −
17.3354 12 𝑇𝐵 ) 10 𝑇𝐵3
(15)
Where: MW: The mean molecular weight of the hydrocarbon, (g/mol). SG60: The average specific gravity of the hydrocarbon at 15oC, as estimated by equation (6) when solved for SG60. TB: The normal boiling point of the hydrocarbon, defined as the temperature of 50% vol. evaporation of the TBP curve, at 100kPa(a) pressure, (K).
Equations (12-14) may be used to calculate the vaporization duty of the hydrocarbon at its normal boiling point. However, since the evaporation of hydrocarbons does not take place at 100kPa(a), the enthalpy of vaporization must be calculated at the operating conditions. For this purpose, Watson correlation (Watson, 1933, 1943) may be used:
𝑇1 0.38 1−𝑇 𝐶 𝛥𝛨𝑉 = 𝛥𝛨𝑉𝐵 ( ) 𝑇𝐵 1−𝑇 𝐶 Where: 13
(16)
ΔΗV: The vaporization duty of the hydrocarbon, at the operating temperature, (Joule/mol) ΔΗVB: The vaporization duty of the hydrocarbon, at its normal boiling point, (Joule/mol) T1: The operating temperature, (K) TB: The normal boiling point of the hydrocarbon, defined as the temperature of 50% vol. evaporation of the TBP curve, at 100kPa(a) pressure, (K)
2.2.3 Heat duty for steam superheating / gas heating
Many fired heaters have one or more steam superheating coils in their convection sections. Moreover, live velocity steam may be injected in the coils of some furnaces. Hydrotreater / hydrocracker furnaces also usually heat hydrogen (or the recycle gas of the unit). Such duties may be calculated by equation (1) if the isobaric specific heat (CP) of each gas is known. For the needs of this paper, Shomate equation, (NIST, 2015), is used for CP.
𝐶𝑃 = 𝐴 + 𝐵𝑡 + 𝐶𝑡 2 + 𝐷𝑡 3 +
𝐸 𝑡2
(17)
Where: Cp: The isobaric specific heat of the gas at temperature T, (J/molK) t: A function of absolute temperature T, t=T/1000, (K) A~E: Constants specific to each gas.
Combining equations (1) and (17), the enthalpy change of gas superheating may be calculated: 𝛥𝛨𝐺𝑆𝐻 = 𝐴(𝑡2 − 𝑡1 ) +
𝐵 2 𝐶 𝐷 1 1 (𝑡2 − 𝑡12 ) + (𝑡23 − 𝑡13 ) + (𝑡24 − 𝑡14 ) − 𝐸( − ) 2 3 4 𝑡2 𝑡1
Where:
14
(18)
ΔΗGSH: The enthalpy change of the gas, heated from T1 to T2, (J/mol) t: A function of absolute temperature T, t=T/1000, (K) A~E: Constants specific to each gas.
Values for the constants A~E are available in the bibliography for a wide range of materials. Tables 1 and 2, (NIST, 2015), (Chase, 1998), may be used for steam and hydrogen.
The next paragraph presents a procedure based on equations (1) - (18) for the calculation of the process side duty of a fired heater.
3. Algorithm
Equations (1) – (18) can be used to calculate the process side (absorbed) duty of a fired heater. The required data are:
Fired heater mass feed rate.
Fired heater velocity steam feed rate (if any).
Fired heater hydrogen feed rate (if any).
Superheater coil steam feed rate (if any).
Feed TBP or other distillation curve.
Feed Specific Gravity at 15.6oC (60oF).
Coil Outlet Temperature and Pressure. In the case of distillation column feed preheat furnaces, the flash zone conditions may be used instead.
Coil inlet temperature. 15
Superheater coil inlet and outlet temperatures, (if any).
Velocity steam inlet temperature (if any).
Hydrogen coil inlet temperature (if any).
The proposed algorithm consists of 18 steps and may be easily used to develop a computer program. The following section describes the steps. The algorithm’s flow chart is depicted in Figure 1. The number on the left of each step in Figure 1 corresponds to the step number in the algorithm description below.
1. If a TBP distillation curve of the feed is available, proceed to step 4. 2. Convert all feed distillation data to TBP distillation curve. The conversion procedures need as input the Watson characterization factor, KW. In case KW is not available, suppose KW = 12. 3. Use the temperature of 50% vol. evaporation of the TBP curve calculated in step #2 as input (T50) for equation (6), to calculate a new value for KW. Return to step #2 and use the new value of KW as input for the calculation of the TBP curve. Repeat steps #2 and 3 until KW is calculated. 4. Calculate the mean molecular weight of the feed, using equation (15). 5. Using the result of step #4, the hydrocarbons feed rate, the coil outlet pressure, the velocity steam feed rate if any and the hydrogen feed rate if any, calculate the partial pressure of the hydrocarbons at the furnace outlet,(PH/C) utilizing equation (8). 6. Use the PH/C calculated in step #5, the KW of either step #1 or step #3 and the TBP curve of the feed at 100 kPa(a), (either from step#1 or #3), to calculate the TBP distillation curve points at the partial pressure of the hydrocarbons, implementing equations (9)-(11).
16
7. Use the TBP curve calculated in step #6 and the coil outlet temperature of the furnace, to calculate the %volume of evaporation (%EV), of the liquid hydrocarbon feed at the coil outlet conditions, by linear interpolation within the points of the step #6 TBP curve. 8. The volume average normal boiling point of the fraction of the feed that was evaporated inside the furnace may be calculated from the original TBP curve, (either step #1 or step #2) as the temperature that corresponds to (%EV)/2 volumetric evaporation. Use (%EV) from step #8 to calculate the volume average normal boiling point of the evaporated fraction of the feed, (TEV50). 9. Use KW of either step #1 or step #3 and the TEV50 calculated at step #8 as input for equation (6), in order to calculate the mean specific gravity of the fraction of the feed that was evaporated inside the furnace. Equation (6) must be rearranged for the calculation of SG60. 10. Use the TEV50 of step #8 and SG60 of step #9 with equations (13) and (14) to calculate the critical properties of the fraction of the feed that was evaporated inside the furnace. 11. Use the critical properties calculated in step #10 and the TEV50 of step #8 as input for equation (12), to calculate the vaporization duty of the fraction of the feed that was evaporated, at its normal boiling point. 12. Use equation (16), to calculate the vaporization duty of the fraction of the feed that was evaporated, at the operating temperature. Other input for this step are TEV50 of step #8, (as the normal boiling point of the hydrocarbon), the critical temperature of step #10 and the operating temperature at the coil outlet. 13. Use the specific gravity of the whole feed and the KW of either step #1 or step #3, with equations (3),(4) and (5) to calculate respectively the parameters A1, A2 and A3.
17
14. Use the coil inlet temperature, the coil outlet temperature and the parameters A1, A2 and A3 from step #13 to calculate the heating duty of hydrocarbons along the coil, with equation (7). 15. Use equation (18), the steam inlet temperature and the coil outlet temperature to calculate the heating duty of the velocity steam, if any. 16. Use equation (18), the steam inlet temperature and the steam outlet temperature to calculate the heating duty of the steam superheating convection coils, if any. 17. Use equation (18), the hydrogen inlet temperature and the coil outlet temperature to calculate the heating duty for the heating of hydrogen, if applicable. 18. Calculate the total absorbed duty of the furnace from the results of steps #12, 14, 15, 16 and 17 and the respective flow rates.
4. Comparison with other methods
The proposed algorithm has been implemented in a computer program. The program has been used to calculate the absorbed duty of existing refinery fired heaters. The absorbed duty of those furnaces has been also calculated by the indirect method and by a commercial rigorous simulation package, using the Soave – Redlich – Kwong equation of state for flash calculation. Table 3 compares the results of the calculations.
The results show that the proposed algorithm has results comparable to a commercial, rigorous simulator. Moreover, both results are very close to those of the usual indirect method. Ta-
18
ble 4 provides the details of the absorbed duty calculation for all 3 cases used in Table 3, per algorithm step. Each line represents the corresponding step’s result.
5. Conclusions and Recommendations.
An algorithm for the calculation of the absorbed, (process side) duty of fired heaters was presented. The required data are usual operating and laboratory data (specific gravity and distillation curve of the feed). The proposed method is easy to implement in a usual spreadsheet and in the same time has accuracy comparable to process simulators and to the indirect method. The results of the proposed method are almost identical to those of absorbed duty calculation by process simulator, for the same set of analytical and operational data.
The correlations used in this work, may be substituted with other, more specific if it is deemed necessary. API Databook, (Daubert and Danner, 1997) correlations for critical properties may be used instead of Kesler – Lee, (Kesler and Lee, 1976) equations, or NASA multi parameter isobaric specific heat correlations instead of Shomate polynomials.
As is the general case of direct method, the absorbed duty calculation is sensitive to errors in flow rate measurement. However, modern refineries use adequate instrumentation and usually are able to provide accurate enough measurements. On the other hand, daily laboratory feed analysis needed for process side characterization, are usually more accurate than field flue gas O2 measurements. Moreover, simultaneous use of direct and indirect method may indicate excessive tramp air ingress and thus aid to equipment efficiency improvement.
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References Arora V.K. Check Fired Heater Performance. Hydrocarbon Processing May 1985; 85-7. Abbi Y.P., Shashank J. Handbook on Energy Audit and Environment Management. New Delhi, India: The Energy and Resources Institute, TERI; 2009. American Society of Mechanical Engineers (ASME) Performance Test Code for Steam Generating Units PTC 4.1”, 1974. Chase Jr. M.W., NIST-JANAF Thermochemical Tables. 4th Edition J. Phys. Chem. Ref. Data, Monograph 9, 1998; 1-1951 Daubert T.E., Danner R.P. API Technical Databook – Petroleum Refining. 6th ed. Washington D.C.: American Petroleum Institute (API); 1997. Devakottai B.S. Energy efficiency in furnaces and boilers. In: Rossiter A.P., Jones B.P. Energy Management and Efficiency for the Process Industries. Hoboken: Wiley; 2015. p. 107-27. Edmister W.C., Pollock D.H. Phase Relations for Petroleum Fractions. Chem. Eng. Progr. 1948; vol. 44: 905-26. Ganapathy V. Applied Heat Transfer. 1st ed. Tulsa, Oklahoma: Pennwell Publishing Co.; 1982. Kesler M.G., Lee B. I. Improve prediction of enthalpy of fractions. Hydrocarbon Processing, March 1976; 153 – 8. Lieberman N.P., Lieberman E.T. A Working Guide to Process Equipment. 4th ed. New York: McGraw-Hill; 2014. Linstrom P.J., Mallard W.G., Eds. NIST Chemistry WebBook NIST Standard Reference Database Number 69. National Institute of Standards and Technology, Gaithersburg MD, 20899, http://webbook.nist.gov, (retrieved July 15, 2015). Maxwell J.B., Bonnell L.S. Derivation and Precision of a New Vapor Pressure Correlation for Petroleum Hydrocarbons. Industrial and Engineering Chemistry 1957; 49: 1187- 96. Patel S. Simplify Your Thermal Efficiency Calculation. Hydrocarbon Processing, July 2005; 63-9. Riazi M.R. Characterization and Properties of Petroleum Fractions, American Society for Testing and Materials, 2005. Riedel L. Kritischer Koeffizient, Dichte des gesättigten Dampfes und Verdampfungswärme. Untersuchungen über eine Erweiterung des Theorems der übereinstimmenden Zustände. Teil III. Chemie Ingenieur Technik 1954; 26: 679–83. Trambouze P. Petroleum Refining, Materials and Equipment. 1st ed. Paris: Editions Technip; 2000. 21
Watson K.M., Nelson E.F. Improved Methods for Approximating Critical and Thermal Properties of Petroleum Fractions. Ind. Eng. Chem. 1933; 25 (8): 880–7. Watson K.M. Thermodynamics of the Liquid States, Generalized Prediction of Properties. Ind. Eng. Chem. 1943; 35: 398-406.
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Figure Legends
Figure 1: Algorithm Flow Chart.
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Table 1, Shomate polynomial constants for steam, (NIST, 2015), (Chase, 1998)
Temperature (K) A B C D E F G H
500 - 1700 30.092 6.832514 6.793435 -2.53448 0.082139 -250.881 223.3967 -241.8264
1700 - 6000 41.96426 8.622053 -1.49978 0.098119 -11.15764 -272.1797 219.7809 -241.8264
Table 2, Shomate polynomial constants for hydrogen, (NIST, 2015), (Chase, 1998)
Temperature (K) A B C D E F G H
298 - 1000 33.066178 -11.363417 11.432816 -2.772874 -0.158558 -9.980797 172.707974 0
1000 - 2500 18.563083 12.257357 -2.859786 0.268238 1.97799 -1.147438 156.288133 0
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Table 3, Absorbed duty as calculated by three different methods
Furnace Type
Indirect
Direct
(pro- Direct (Rig-
(kW)
posed
algo- orous Simu-
Case 1, Vacuum distillation furnace, ca- 34,047
rithm) (kW)
lation) (kW)
34,342
34,265
10,940
10,633
42,644
41,061
thedral type, 2 radiant sections, common convection section, with velocity steam and 2 convection coils for low and medium pressure steam superheating. Case 2, Diesel hydrotreater feed & recycle 10,813 gas, Vertical cylindrical type. Case 3, Vacuum distillation furnace, ca- 42,439 thedral type, 2 radiant sections, common convection section, with velocity steam and 2 convection coils for low and medium pressure steam superheating.
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Table 4, Details of the absorbed duty calculation for all 3 cases used in Table 3.
Step #
units
1 2 3 4 5 6 7 8 9
unitless g/mol kPa(a) %vol K
10
K ; kPa
11 12
kJ/kg kW
13
unitless
14 15 16 17 18
kW kW kW kW kW
Case 1 No, ASTM D1160 available ok 11.761 562.62 2.753 ok 56% vol 717.6 0.9260 Tc=914.2 K ; Pc=1,123.75 kPa 185.35 11321.3 A1=0.996839; A2=0.385728; A3=0.0005215 28,962.9 323.9 2,036.2 Not applicable 42,644.2
Case 2 No, ASTM D-86 Available ok 11.792 223.08 733.865 ok 37% vol 490.0 0.8133 Tc=730.5 K ; Pc=2,171.39 kPa 233.26 1538.3 A1=0.998533; A2=0.421425; A3=0.000557 8,009.5 Not applicable Not applicable 1,392.0 10,939.8
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Case 3 No, ASTM D1160 available ok 11.885 644.05 2.642 ok 45% vol 712.0 0.9139 Tc=910.0 K ; Pc=1,099.11 kPa 156.25 5942.8 A1=1.003666; A2=0.384465; A3=0.00052 27,256.0 198.7 944.8 Not applicable 34,342.3