## Brazilian Journal of Chemical Engineering

*On-line version* ISSN 0104-6632

### Braz. J. Chem. Eng. vol. 15 no. 1 São Paulo Mar. 1998

#### http://dx.doi.org/10.1590/S0104-66321998000100006

**A METHOD FOR EXERGY ANALYSIS OF SUGARCANE BAGASSE BOILERS**

**L.A.B. CORTEZ and E.O. GÓMEZ**

School of Agricultural Engineering - State University of Campinas

CEP 13083-970 - Campinas, SP - Brazil

E-Mail: cortez@agr.unicamp.br - Phone: 019-788 2033 - Fax: 019-788 2090

(Received: April 15, 1997; Accepted: December 11, 1997)

**Abstract - **This work presents a method to conduct a thermodynamic analysis of sugarcane bagasse boilers. The method is based on the standard and actual reactions which allows the calculation of the enthalpies of each process subequation and the exergies of each of the main flowrates participating in the combustion. The method is presented using an example with real data from a sugarcane bagasse boiler. A summary of the results obtained is also presented together based on the 1^{st} Law of Thermodynamics analysis, the exergetic efficiencies, and the irreversibility rates. The method presented is very rigorous with respect to data consistency, particularly for the flue gas composition.** **

*Keywords*: Exergy, boiler efficiency, bagasse combustion.

INTRODUCTION

The thermodynamic analysis of sugarcane bagasse boilers is not a common practice in Brazil. Although the process of bagasse combustion represents most important sources of irreversibilities, this subject has not received sufficient attention because saving bagasse is not yet a top priority in the Brazilian sugar industry. Several authors have studied and developed methods to conduct thermodynamic analysis. However the majority of the published works are based on the 1^{st }Law analysis, such as that presented by Babcock and Wilcox (1978), Beatón-Soler and Silva-Lora (1991), Hugot (1978), IPT (1990) and Pera (1990). The main disadvantage of these methods is that they are based on a "quantitative" approach therefore do not consider the quality differencies between temperature levels. Therefore, some authors have proposed and studied a thermodynamic performance using "exergy" as a tool (Serrano, 1987;Peres, 1982). Based on these experiments, a method is proposed here which uses concepts derived from both the 1^{st} and 2^{nd} Laws combined, known as the exergy method, for the thermodynamic analysis of boilers using wet sugarcane bagasse as a fuel.

The Exergy Method for Sugarcane Bagasse Boilers

The method presented was originally developed by Jordan (1988) for Texas lignite fired boilers. For the thermodynamic analysis of sugarcane bagasse boilers, first a standard reaction for firing wet bagasse (without ash) is presented. Then, the standard reaction is compared with the actual reaction, using data collected in a Zanini/Foster-Wheeler model ZFW - SF150 bagasse boiler with 80 t vapor/h nominal capacity installed at a sugar mill near Campinas, SP, Brazil. Specific features of the boiler, such as grill type, temperature and profile during combustion, are not included because this method allows a thermodynamic analysis of the whole boiler as a system, considering only the main flowrates crossing the control volume. A simplified view of the boiler is presented in Figure 1.

**Figure 1:** Simplified view of main mass flowrates for a bagasse boiler: bagasse (f), air (a), gases (g), ash (s), feeding water (w_{1}) and high pressure steam (w_{2})

In order to conduct the exergy method, it was necessary to obtain actual samples from the boiler to be studied. The samples were made for the fuel (wet bagasse), the particulate and the ash. The samples were analyzed for their composition and the data are presented in Tables 1 and 2.

Bagasse

In Table 3 the dried bagasse mass fractions (m_{f}) obtained from the ultimate analysis are presented. The wet bagasse mass fraction, or" as fired" bagasse, as well as the wet ashless bagasse mole fractions (y_{ab}) is also presented.

Table 1: Average composition (Proximate Analysis) of samples of wet bagasse, particulate and ash

Proximate Analysis | Heating Value | |||||

Moisture, % | Volatile Matter, % | Fixed Carbon, % | Ash, % | HHV, kJ/kg | LHV, kJ/kg | |

Bagasse | 49.9 ± 2.8 | 81.7 ± 0.5 | 15.7 ± 0.6 | 2.5 ± 0.1 | 16793 ± 244 | 6484 ± 568 |

Particulate | 0.8 ± 0.3 | 6.1 ± 2.0 | 30.2 ± 23.4 | 63.7 ± 25.1 | 11170 ± 3523 | 10758 ± 3408 |

Ash | 89.0 ± 1.3 | 8.0 ± 0.5 | 79.8 ± 1.5 | 12.2 ± 1.5 | 26239 ± 115 | 698 ± 348 |

* Analysis were done in the Laboratory for Alternative Fuels (LCA) of the Physics Institute at the State University of Campinas-UNICAMP, Brazil. The results are based on dry matter and the reproducibility is on the order of 2%.

Table 2: Average composition (Ultimate Analysis) of samples of wet bagasse, particulate and ash

Ultimate Analysis | |||||

Hydrogen, % | Carbon, % | Oxygen, % | HHV, kJ/kg | LHV, kJ/kg | |

Bagasse | 6.8 ± 0.1 | 45.3 ± 1.3 | 45.4 ± 1.7 | 16793 ± 244 | 6484 ± 568 |

Particulate | 1.4 ± 0.7 | 31.5 ± 26.0 | 4.0 ± 1.2 | 11170 ± 3523 | 10758 ± 3408 |

Ash | 2.6 ± 0.4 | 79.8 ± 1.4 | 5.4 ± 0.9 | 26239 ± 115 | 698 ± 348 |

* Analysis were done in the Laboratory for Alternative Fuels (LCA) of the Physics Institute at the State University of Campinas-UNICAMP, Brazil. The results are based on dry matter and the reproducibility is on the order of 2%.

Table 3: Mass fractions of dried and wet, or" as fired," bagasse and mole fractions (y_{ab}) of the wet ashless bagasse

Component | m | m | m | M kg/kmole | m | y |

C | 0.453 * | 0.227 * | 0.230 * | 12.011 | 0.019 * | 0.268 * |

H | 0.068 * | 0.034 * | 0.034 * | 2.016 | 0.017 * | 0.239 * |

O | 0.454 * | 0.227 * | 0.230 * | 32.000 | 0.007 * | 0.099 * |

Ash | 0.025 * | 0.013 * | 0.013 | n.a. | n.a. | n.a. |

H | 0.996 = j | 0.499 * | 0.506 * | 18.015 | 0.028 | 0.394 * |

Total | 1.996 | 1.000 | 1.013 | n.a. | 0.071 | n.a. |

S * | * 1.000 | * 1.000 | * 1.000 | n.a. | * 0.043 | n.a. |

obs:

- the values followed by * are added at the S line.

- the values with * add 1.0; the "j" value is calculated as j = 0.499 [ 1+j]

Then, the wet ashless bagasse mole (M_{wab}) = 1/0.071 = 14.085 kg wab/kmole wab and the dry ashless bagasse mole (M_{dab}) = 1/0.043 = 23.256 kg dab/kmol dab can be calculated.

Air

For the atmospheric air used for combustion, the conditions were dry bulb temperature (T_{db}) = 25° C; relative humidity (f ) = 60%; barometric pressure (P) = 100 kPa; and water vapor parcial pressure (p_{w}) = f . p_{sat} (T_{db}) = 0.6 . 3.1693 = 1.902 kPa (Table 4).

The absolute humidity (w) can be calculated as w = 0.622 . p_{w}/p_{a} = 0.012 kg H_{2}O/kg dry air and molar absolute humidity () = p_{w}/p_{a} = 0.019 mole H_{2}O/mole dry air. w Therefore, with calculations in Table 4, it is possible to obtain mole fraction values for every component of the air (y_{i}) in relation to the mole** **fraction of oxygen (y_{o}).

Standard Reaction

With this data, compiled in Tables 3 and 4, is possible to write the standard reaction, defined as "complete" it (without CO and without C in the combustion products) as : [ wet ashless bagasse] + [ dry air] with the condensation water formed:

[ 0.268 C + 0.239 H_{2} + 0.099 O_{2} + 0.394 H_{2}O + Ash] +

+ a [ 3.718 N_{2} + O_{2} + 0.044 Ar] ® (1)

® b CO_{2} + c H_{2}O + d N_{2} + e Ar

by calculating the coefficients:

[ 0.268 C + 0.239 H_{2} + 0.099 O_{2} + 0.394 H_{2}O + Ash] +

+ [ 1.075 N_{2} + 0.289 O_{2 }+ 0.013 Ar] ® (2)

® [ 0.268 CO_{2} + 0.633 H_{2}O + 1.075 N_{2} + 0.013 Ar]

Then, as 1.377 *kmoledryair/ kmolewab*, it is possible to calculate the theoretical air/fuel relation (TAFR) as follows:

(3)

Therefore TAFR = 2.753 kg dry air/kg wet bagasse.

Actual Reaction

Combustion gas product composition was determined for CO and O_{2} using the "TESTO 33" continuous measuring equipment manufactured by KRON. The average CO and O_{2} contents, taken at 15 minute intervals were 0.3% and 4.2%, respectively. The CO_{2} content was calculated using a volumetric chart for dry combustion gases by Babcock and Wilcox (1978). This chart allows the calculation of the CO_{2} content using CO and O_{2} data, and the maximum CO_{2} value by considering the burned bagasse. This value of CO_{2max} can be calculated using the following equation:

(4)

Therefore, the CO_{2max} calculated for the bagasse mass fraction composition (Table 3 is 19.74%. Using equation (5) the CO_{2} content for incomplete combustion can be calculated:

(5)

Table 4: Mole composition of the atmospheric air used for combustion and the relation between the mole fraction of components and that of oxygen (y_{i}/y_{0})

Component | y | y | M | y.M | m | yi/yo |

N | 0.781 * | 0.766 * | 28.016 | 21.460 * | 0.755 | 3.718 |

O | 0.210 * | 0.206 * | 32.000 | 6.592 * | 0.232 | 1.000 |

Ar | 0.009 * | 0.009 * | 39.944 | 0.359 * | 0.013 | 0.044 |

H | 0.019 | 0.019 | 18.016 | 0.342 | 0.012 | 0.092 |

Total | 1.019 | 1.000 | n.a. | n.a. | 1.000 | n.a. |

S * | * 28.411 |

The CO_{2} content in the air is considered insignificant^{ }(< 0.1%).

The result is CO_{2} = 15.59%. The incomplete combustion equation, called the actual reaction between [ wet bagasse] + [ humid air] , can be established as follows:

[ 0.268 C + 0.239 H_{2} + 0.099 O_{2} + 0.394 H_{2}O + Ash] +

+ a [ 3.718 N_{2} + O_{2} + 0.044 Ar + 0.092 H_{2}O] ®

® b C + c CO + d CO_{2} + e H_{2}O + f O_{2} + g N_{2} + (6)

+ h Ar + Ash

Therefore, the sum of gaseous products of combustion coefficients, in a dry basis, (x) is given by:

x = c + d + f + g + h (7)

Based on the measured flue gas composition (TESTO readings) that d = 0.156 x ; and c = 0.003 x ; and f = 0.042 x, then g + h = 0.799 x. From Table 4 we have that g = 3.718 a and h = 0.044 a, thus x = 4.708 a.

Substituting these values in the components equation, it is possible to determine the remaining coefficients and to obtain the actual equation for incomplete combustion, as follows:

[ 0.268 C + 0.239 H_{2} + 0.099 O_{2} + 0.394 H_{2}O + Ash] +

+ [ 1.253 N_{2} + 0.337 O_{2} + 0.015 Ar + 0.031 H_{2}O] ®

® [ 0.015 C + 0.005 CO + 0.248 CO_{2} + 0.664 H_{2}O + (8)

+ 0.067 O_{2} + 1.253 N_{2} + 0.015 Ar + Ash]

From this equation we have that 1.605 *kmoledryair/ kmolewab* and the actual air/fuel ratio (AAFR):

So, the excess air (l ), defined by [ AAFR - TAFR] /TAFR, is l = 16.5%.

The actual combustion process in the boiler may be written as:

(9)

The indexed temperatures indicates actual conditions. The equation (9) may be represented by equations (10) to (16) with the aid of a thermodynamic path:

(10)

The molar enthalpy variation in the process () is given by equation (10) as (T_{2} – T_{1}). Adopting an average c_{n} of 2.968 kJ/kg wab° C for the bagasse (IPT, 1990), and 14.085 kg wab/kmole wab results in = 217.7 kJ/kmole wab. The standard conditions were adopted 25^{o}C and 100 kPa.

(11)

To determine molar enthalpy () for equation (11), the mole fraction values (y) and the IDGAS software developed by Jordan (1988) should be used, obtaining values of for the air. Therefore, = ., i.e. = 322.6 kJ/kmole wab and . = 16.32 kJ/kmole wab.

(12)

This standard reaction is applied to the LHV. With 50% moisture wet basis, the LHV is 7,629 kJ/kg. Therefore, the molar enthalpy for eqution (12) is given by the LHV. Using M_{wab}, we get = 107,454.4 kJ/kmole wab.

Using the Szargut and Styrylska equations (Gaggioli, 1980), the exergy calculated the exergy for bagasse based on the last analysis (Table 3) and LHV, and = 9,890.7 kJ/kg is obtained. Therefore, . = and . = 139,310.5 kJ/kmole wab.

(13)

With the stoichiometric coefficients of actual combustion gases, obtained by the equation (8), it is possible to obtain the respective molar fractions (y) and, consequently, values of using the IDGAS software.

Then, calculating molar enthalpy for equation (13), we get = -9,005.7 kJ/kmole wab and = 8,726.7 kJ/kmole.

(14)

The ash specific heat (c_{pash}) is 0.836 kJ/kg° C (Hugot, 1978). The ash enthalpy variation for equation (14) is given by:

(14a)

Thus, = -132.1 kJ/kmole wab. The ash molar exergy, , is given by:

(14b)

where -132.1 kJ/kmole wab; 0.314 kJ/kmole K; __ = 0 for the ash; and C + O _{2}__ ® CO

_{2}; = -394.657 kJ/kmole for carbon (Atkins, 1986). Therefore, . = -6,145.6 kJ/kmole wab.

(15)

Substituting in equation (15):

(16)

= -7,357.6 kJ/kmole is calculated according to data obtained in Atkins (1986). Table 5 summarizes results from partial calculations.

Having given that: = 70,000 kg steam/h, hw1 (100° C; P_{adopted} = 2.23 MPa) = 420.64 kJ/kg, and hw2 (300° C; P_{measured}= 2.03 MPa) = 3,022.60 kJ/kg we have evaluated the power transferred to the steam () which is 50.6 MW. The power utilized () can also be calculated by , given that ; therefore, = 28.4 t wet bagasse/h and = 60.2 MW. Then, the 1^{st} Law efficiency (h ) according to the ASME (1964) is 84.05%.

To perform the exergetic calculation, we need to multiply the molar exergies by the correspondent molar flowrate (0.55 kmole wab/s for bagasse, air, gas and ash). The specific exergies of water and steam are obtained from WATER software by Jordan (1988). These values are then totaled, using feeding water and steam flowrates of 19.44 kg/s. Table 6 presents a summary of main exergy flowrates.

Therefore, the process irreversibility (), here defined as the overall difference between inlet and outlet exergy flowrates, is 49.8 MW. The exergetic efficiency (), defined as the net exergy variation in the water (19.0 MW) over the net exergy used in the process (68.8 MW), is 27.6%.

Table 5: Results of enthalpies of actual combustion reactions, see equation (9)

Enthalpy of Reaction | |

Wet Bagasse from T to Tstandard conditions | + 217.7 |

Actual Air from T to Tstandard conditions | + 322.6 |

Standard Reaction at Standard Conditions | + 107,454.4 |

Combustion Gas Products from Tstandard conditions to T | - 9,005.7 |

Unburnt Solids | - 132.1 |

Gas Products | -7,357.6 |

Total | 91,499.3 |

**Table 6: Results of main exergy flowrates for the bagasse combustion**

Flowrate | Exergy (MW) |

Wet Bagasse (f) | 77.0 * |

Air (a) | 0 * |

Gas Products (g) | 4.8 * |

Ash (s) | 3.4 * |

Feeding Water (w1) | 0.7 ** |

High Pressure Steam (w2) | 19.7 ** |

Balance * (77.0-4.8-3.4) | 68.8 |

Balance ** (19.7-0.7) | 19.0 |

DISCUSSION AND CONCLUSIONS

The method presented for a thermodynamic analysis of sugarcane bagasse boilers is very rigorous with respect to data consistency, specifically for mass balance of the actual equation.

To conduct a similar analysis, high sensitivity, specially for the actual combustion equation must be considered in acquiring data. Small experimental errors are sufficient to cause important deviations, notably in flue gas composition determination.

The results obtained indicated that 1^{st} Law efficiency is high (84.05%). However, the irreversibility rate 49.8 MW is also significant, demonstrating that circa 70% of the fuel exergy is actually destroyed in the combustion process.

Further research is still required to investigate the causes of irreversibility and to determine economic opportunities for reducing it. Finally, the exergetic analysis will become a more effective optimization tool specially when electricity rates become more realistic or when there are more attractive opportunities for saving the bagasse.

NOMENCLATURE

a Air stream

AAFR Actual Air/Fuel Ratio, kg humid air/kg wet bagasse

a,b,c,d,

e,f,g,h,j Auxiliary variables

Maximum mass percentage of CO_{2} in gas products of combustion, %

c_{n }Specific heat of bagasse, kJ/kg wab ° C

c_{n ash }Specific heat of ash, kJ/kg ash ° C

Molar specific heat of bagasse, kJ/kmole wab ° C

dab "dry ashless bagasse"

ex Specific exergy of bagasse, kJ/kg

Molar exergy of ash, kJ/kmole ash

Molar exergy of air, kJ/kmole

Molar exergy at ambient temperature (To), kJ/kmole

Molar exergy for the gas combustion products, kJ/kmole gas

f Fuel (bagasse) stream

g Flue gas stream

Molar Gibbs free energy at To, kJ/kg

Molar enthalpy of air, kJ/kmole

Molar enthalpy at ambient temperature (T_{o}), kJ/kmole

Molar enthalpy at reference temperature (T_{ref}), kJ/kmole

h_{w1}, h_{w2 }Enthalpy of water, kJ/kg

HHV High Heating Value, kJ/kg

Irreversibility rate, MW

IDGAS Software used to obtain the thermodynamic properties of a given gas mixture

LHV Low Heating Value, kJ/kg

Mass flowrate of bagasse, t/h

M Molecular weight, kg/kmole

M_{dab} Molecular weight of dry ashless bagasse, kg dab/kmole dab

M_{wab} Molecular weight of wet ashless bagasse, kg wab/kmole wab

m_{f} Mass fraction

Mass flowrate of steam, kg/h

Number of moles of dry air, kmole dry air

Nnumber of moles of humid air, kmole humid air

Number of moles of dry ashless bagasse, kmole wab

Number of moles of wet bagasse, kmol of wet bagasse

Number of moles of gas from combustion, kmol gas

Number of moles of solids (ash), kmole solids

P Barometric pressure, kPa

p_{a} Air partial pressure, kPa

p_{sat} Saturation pressure at T_{db}, kPa

p_{w} Water vapor partial pressure, kPa

Power transferred to steam, MW

Power from bagasse combustion, MW

s Ash stream

Molar entropy of air, kJ/kmole ° C

Molar entropy at ambient temperature (T_{o}), kJ/kmole ° C

Molar entropy at reference temperature (T_{ref}), kJ/kmole ° C

TAFR Theoretical Air/Fuel Ratio, kg dry air/kg wet bagasse

T_{o} Ambient temperature, ° C

T_{db }Dry bulb air temperature, ° C

w Air absolute humidity, kg H2O/kg dry air

Molar air absolute humidity, mole H_{2}O/mole dry air

w1 Feeding water stream

w2 High pressure steam stream

wab Indicates "wet ashless bagasse"

x Auxiliary variable

y Mole fraction

y_{ab} Ashless bagasse mole fraction

yi Mole fraction for the air component i

y_{0} Oxygen molar fraction

Molar enthalpies of reaction, kJ/kmole

h 1st Law efficiency, %

l Excess air, %

f Air relative humidity, %

_{ex} Exergetic efficiency, %

ACKNOWLEDGMENTS

The author wishes to thanks FAPESP, Foundation for Scientific Research of the State of São Paulo, for supporting this research.

REFERENCES

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