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Properties of chicken manure pyrolysis bio-oil blended with diesel and its combustion characteristics in RCEM, Rapid Compression and Expansion Machine

  • Received: 03 March 2014 Accepted: 25 June 2014 Published: 30 June 2014
  • Bio-oil (bio-oil) was produced from chicken manure in a pilot-scale pyrolysis facility. The raw bio-oil had a very high viscosity and sediments which made direct application to diesel engines difficult. The bio-oil was blended with diesel fuel with 25% and 75% volumetric ratio at the normal temperature, named as blend 25. A rapid compression and expansion machine was used for a combustion test under the experimental condition corresponding to the medium operation point of a light duty diesel engine using diesel fuel, and blend 25 for comparison. The injection related pressure signal and cylinder pressure signal were instantaneously picked up to analyze the combustion characteristics in addition to the measurement of NOx and smoke emissions. Blend 25 resulted in reduction of the smoke emission by 80% and improvements of the apparent combustion efficiency while the NOx emission increased by 40%. A discussion was done based on the analysis results of combustion.

    Citation: Sunbong Lee, Shaku Tei, Kunio Yoshikawa. Properties of chicken manure pyrolysis bio-oil blended with diesel and its combustion characteristics in RCEM, Rapid Compression and Expansion Machine[J]. AIMS Energy, 2014, 2(3): 210-218. doi: 10.3934/energy.2014.3.210

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  • Bio-oil (bio-oil) was produced from chicken manure in a pilot-scale pyrolysis facility. The raw bio-oil had a very high viscosity and sediments which made direct application to diesel engines difficult. The bio-oil was blended with diesel fuel with 25% and 75% volumetric ratio at the normal temperature, named as blend 25. A rapid compression and expansion machine was used for a combustion test under the experimental condition corresponding to the medium operation point of a light duty diesel engine using diesel fuel, and blend 25 for comparison. The injection related pressure signal and cylinder pressure signal were instantaneously picked up to analyze the combustion characteristics in addition to the measurement of NOx and smoke emissions. Blend 25 resulted in reduction of the smoke emission by 80% and improvements of the apparent combustion efficiency while the NOx emission increased by 40%. A discussion was done based on the analysis results of combustion.


    1. Introduction

    In 2030, industrial water consumption is expected to account for 22% of global water demand [1]. The water shortage and poor water quality in some industrial regions have caused the creation of new environmental policies focused on recycling and reuse of water [2].

    Textile industry is one of the largest consumers of water due especially to their finishing processes such as dyeing and subsequent washing steps. High water consumption in textile industry has led to the treatment and reuse of its wastewater [2]. In addition to the presence residual dyes, textile wastewater is characterized by high organic and inorganic matters, turbidity, pH and in some cases, content of toxic chemicals [3].

    Nowadays, biological [4,5,6] and physical-chemical processes [7,8] are used to remove dyes from textile wastewater. However, none of them enables water reuse in textile processes. On the other hand, advanced oxidation processes such as photo-Fenton [9] and photocatalytic [10] have been also studied. Although these methods provided high color removal, the treatment cost is their main limitation.

    Electrochemical processes have also been tested to remove dyes from textile effluents. The process occurs via two pathways: direct anodic oxidation or indirect oxidation. In the direct oxidation, the electrolysis takes place directly on the anode whereas the base of the indirect oxidation is the electrogeneration in situ of the oxidant species that can degrade the pollutants [11]. The main advantage of the electrochemical treatment is that the electron is the only reagent required for the degradation of the pollutants.

    Reactive dyes are the most consumed dyes in the textile industry. These dyes have high washing fastness as they react chemically with the fiber. However, part of reactive dyes can also react with water, generating the hydrolyzed form of the dye that cannot react with the fiber. Then, the hydrolyzed dyes are discharged with the wastewater [12]. To increase the affinity of the dye with the fiber, high amount of salt is added in the dyeing process. Between 0.6 and 0.8 kg of salt/kg of fiber is required, depending on the dye structure, shade and dyeing method [13]. As a result, the wastewater generated in the dyeing process with reactive dyes is characterized by high salt content. This represents an important disadvantage since there is no treatment that enables to destroy the salts. Currently, the treatments used for the removal of salts are based on obtaining a concentrate that must be subsequently removed as a waste. Therefore, wastewater from reactive dyeing process is suitable to be treated by means of electrochemical treatment. No chemicals should be added, as the treatment uses the salts already present in the effluent to generate the oxidant species [14] which destroy the chromophore groups of the dyes, according to the following reactions [15]:

    $ 2{\rm{C}}{{\rm{l}}^ - } \to {\rm{C}}{{\rm{l}}_{2({\rm{aq}})}} + 2{{\rm{e}}^ - } $ (1)
    $ {\rm{C}}{{\rm{l}}_{2({\rm{aq}})}} + {{\rm{H}}_2}{\rm{O}} \to {\rm{Cl}}{{\rm{O}}^ - } + {\rm{C}}{{\rm{l}}^ - } + 2{{\rm{H}}^ + } $ (2)
    $ {\rm{Dye}} + {\rm{Cl}}{{\rm{O}}^ - } \to {\rm{dye}}\;{\rm{fragments}} $ (3)

    According to the reaction (2), the chloride ion is obtained again at the end of the process and can be oxidized to reinitiate a new process. Some residual oxidants can remain in solution after the oxidation of dyes. The UV irradiation is applied to achieve its removal, providing a saline solution able to be reused in new dyeing processes.

    Taking these considerations into account, the aim of this work is to study the feasibility of the electrochemical techniques combined with UV to treat industrial effluents from the dyeing process with reactive dyes. Once the effluents have been decolorized by electrochemical treatment, are reused in new cotton dyeings. Finally, fabrics dyed with the reused effluent are evaluated with respect to references carried out with softened tap water.


    2. Experimental


    2.1. Reagents

    Three reactive dyes (DyeStar) were selected for the study of effluent reuse: Procion Yellow H-EXL (PY), Procion Crimson H-EXL (PC) and Procion Navy H-EXL (PN). Table 1 shows the description of the dyes used in this study [12]. Sodium carbonate (Sigma-Aldrich) and sodium chloride (Scharlab) were used in the dyeing procedure. Finally, before the dyeing process, pH of treated effluents was adjusted with solutions of NaOH and HCl.

    Table 1. Description of the dyes used in this study.
    Dye C.I. name Chromophore Reactive group
    PY Reactive Yellow 138:1 Diazo Monoclorotriazinc
    PC Reactive Red 231 Diazo Monoclorotriazinc
    PN Non-registered Diazo Monoclorotriazinc
     | Show Table
    DownLoad: CSV

    2.2. Wastewater

    Five industrial effluents supplied by a textile mill were selected to be treated. They were collected from the jet dyeing process.


    2.3. Electrochemical treatment assisted by UV

    The effluents (0.5 L for each experiment) were treated in an undividable electrolytic cell. In all cases, the intensity was set at 10 A. The electrodes were made of Ti/PtOx, with 44.8 cm2 of active surface. The UV radiation was performed with a Philips TUV lamp PL-S UV-C at 254 nm and 9 watts.


    2.4. Effluent reuse

    Before reusing the treated effluent, a reconstitution step must be performed. The effluent reconstitution is carried out in the following steps:

    ● Carbonates and bicarbonates are removed by acid addition and stripping.

    ● Neutralization of the effluent by alkali addition.

    ● Residual oxidants removal with UV irradiation.

    Once the bath is reconstituted, the concentration of chloride ion should be quantified in order to determine to amount to be added in the reuse dyeing process.

    The reuse dyeing tests were performed in a laboratory Ti-Color dyeing machine (Integrated Color Line) under the following conditions: 10 g of cotton fabric, dye concentration 3% o.w.f (over weight of fiber), liquor ratio 1:10 (1 g fiber/10 mL dye bath), 80 g·L–1 of NaCl and 16 g·L–1 of Na2CO3. The dyeing method is shown in Figure 1.

    Figure 1. Dyeing method.

    After the dyeing process, a washing process in nine steps was carried out:

    ● 1st–3rd: Cleaning with softened tap water at 50 ℃ during 10 min.

    ● 4th: Soap cleaning with 2 g/L of COTEMOLL TLTR at 95 ℃ during 15 min.

    ● 5th: Cleaning with softened tap water.

    ● 6th: Soap cleaning

    ● 7th–9th: Cleaning with softened tap water.

    All the experiments were performed at liquor ratio 1:10.


    2.5. Analytical methods and measurements

    COD was determined according to the methods recommended by American Public Health Association [16]. The COD removal was calculated using the following equation:

    $ COD\;removal\left( \% \right) = \frac{{\left( {CO{D_0} - CO{D_f}} \right)}}{{CO{D_0}}} \cdot 100 $

    where COD0 is the value before the electrochemical treatment and CODf is the value after the electrochemical treatment.

    The conductivity and pH were determined using a Conductimeter GLP 31 (CRISON) and a pHmeter GLP 21 (CRISON) respectively [16].

    Color removal was calculated from the initial absorbance (A0) and the absorbance at the end of the treatment (Af) using the following equation:

    $ Colour\;removal\left( \% \right) = \frac{{\left( {{A_0} - {A_f}} \right)}}{{{A_0}}} \cdot 100 $

    Absorbance was determined with a UV–visible spectrophotometer (UV-2401, Shimadzu Corporation) at the maximum wavelength of the sample visible spectrum.

    The determination of Cl was carried out with Ion Chromatography ISC-1000 (Dionex) [16].

    Finally, the quality of dyed fabrics was determined in conformity with the Standard UNE-EN ISO 105-J03 [17]. Total color differences (DECMC(l:c)) were calculated from lightness (DL*), chroma (DC*) and Hue (DH*) using the following equation:

    $ {\rm{D}}{{\rm{E}}_{{\rm{CMC}}({\rm{l}}:{\rm{c}})}} = {\rm{ }}{[{\left( {{\rm{DL}}*/{\rm{l}}{{\rm{S}}_{\rm{L}}}} \right)^2} + {\left( {{\rm{DC}}{*_{{\rm{ab}}}}/{\rm{c}}{{\rm{S}}_{\rm{c}}}} \right)^2} + {\left( {{\rm{DH}}{*_{{\rm{ab}}}}/{{\rm{S}}_{\rm{H}}}} \right)^2}]^{1/2}} $

    For the measurements, a Macbeth Color Eye 7000A spectrophotometer was used. They were performed with the standard illuminant D65/10˚. In general, a dyeing is considered into the acceptance range when the DECMC(l:c) value with respect to a reference sample is lower than 1.


    3. Results and discussion


    3.1. Wastewater characterization

    Before the electrochemical treatment, the effluents were characterized. The characteristics of each effluent are shown in Table 2.

    Table 2. Characterization of samples of effluents collected from Jet process.
    Initial Effluent COD (mg·L–1) Conductivity (mS/cm) pH Cl (mg·L–1) λmax
    A 3518.9 57.5 10.9 24203.7 543.5
    B 1515.4 83.1 10.6 66223.2 588.5
    C 1099.0 88.3 10.7 39049.9 511.0
    D 2450.5 129.0 10.5 69064.6 427.0
    E 1811.0 124.1 10.7 65952.2 519.0
     | Show Table
    DownLoad: CSV

    As can be observed in Table 2, the effluents from Jet dyeing process presented alkaline pH and high conductivity. In addition, the concentrations of Cl are between 24 and 70 g·L–1, that represents a concentration up to 115 g/L of NaCl.


    3.2. Electrochemical treatment

    The efficiency of the electrochemical technique applied to treat textile effluents from Jet dyeing processes was determined by characterizing of treated effluent (Table 3).

    Table 3. Characterization of effluents from Jet process after 10 min of electrochemical treatment.
    Treated Effluent Conductivity (mS/cm) pH COD removal (%) Color removal (%)
    A 63.0 10.6 11.9 100
    B 77.7 10.2 0.0 100
    C 87.1 10.7 0.0 100
    D 128.1 10.7 51.4 100
    E 120.6 11.2 8.3 100
     | Show Table
    DownLoad: CSV

    In all cases, the effluents were totally discolored after 10 min. of electrochemical treatment (Figure 2).

    Figure 2. Electrochemical discoloration of textile effluents.

    Regarding COD values, the reduction of organic matter did not follow a clear trend, as COD removal rates up to 51% were obtained. A full mineralization could be achieved with a longer treatment time [18]. However, other methods, such as biological treatments, are more efficient for this purpose. The electrochemical treatment is able to break down the poorly biodegradable organic molecules such as dyes into dye fragments, improving the biodegradability of the effluents [19]. Consequently, a full mineralization of the effluents could be achieved with a combination of electrochemical processes with conventional biological treatments.

    At the end of the treatment, pH and conductivity values remained very similar to the initial ones. In some cases, these values are almost constant which evidences that the electrochemical treatment has little influence on them.

    The concentration of residual oxidants at the end of the treatment is a key factor when the electrochemical treatment is carried out for reuse since they must be removed before reusing the treated effluent. Consequently, the treatment should be carried out at intensity high enough to achieve a good discoloration, but as lower as possible in order to avoid the generation of residual oxidants.

    The optimization of the residual oxidants at the end of the treatment was carried out with the effluent C. It was treated at 2 A and 10 A, and the residual oxidants were determined in both cases. Results are presented in Table 4.

    Table 4. Results obtained in the treatment of effluent C at different values of intensity and time of treatment.
    Intensity (A) Treatment time (min) Color removal (%) Residual oxidants (mg·L–1)
    2 30 93 0
    2 60 97 2
    10 10 100 2000
     | Show Table
    DownLoad: CSV

    As it was expected, decreasing the intensity resulted in increasing the time required to decolorize the effluent. However, the concentration of residual oxidants was also significantly reduced. On the other hand, the two trials at 2 A evidence that the first 30 minutes of treatment provided very high discoloration rate (93%) whereas in the last 30 minutes the color removal increased only in 4% (97% total color removal). Thus, when the time of treatment (and the power consumption) is increased twice, the color removal yield is only increased in 4%.

    Taking into account these results, it was decided to carry out the reuse tests with the effluent C treated for 30 minutes at 2 A.


    3.3. Effluent reuse

    On the bases of our previous studies, the reuse process was carried out with 70% of decolored effluent, which also contains 64% of residual salt.

    Cotton samples dyed with the 70% uncolored effluent was evaluated with respect to reference dyeings performed with decalcified water. Their chromatic coordinates and color differences (DECMC(2:1)) are shown in Table 5.

    Table 5. Chromatic coordinates and color differences values.
    Dye DH DL DC DECMC(2:1)
    PC –0.55 0.37 –0.37 0.76
    PN –0.11 0.22 –0.33 0.41
    PY –0.58 –0.29 0.67 0.93
     | Show Table
    DownLoad: CSV

    It can be seen that DECMC(2:1) values, which reflects the human eye perception, were lower than 1, the tolerance limit generally accepted by the textile industry (Figure 3).

    Figure 3. Results obtained in the effluent reuse study.

    3.4. Advantages of the industrial implementation of the process

    The combination of electrochemical technique with UV irradiation to treat and reuse textile wastewater has clear environmental and economic advantages.

    According to the dyeing method, 10 L of water and 0.5 kg of salt are required to dye 1 kg of textile product. Consequently, the reuse of 70% of water and 64% of salt in the dyeing process result in a saving of 7 L of water and 0.5 kg of salt per kilogram of textile product.

    A medium size textile mill can produce from 1–5 Tm of reactive dyed fabric per day. This would imply the generation of 10–50 m3 of exhausted dyebaths to be treated. The implementation of combined electrochemical and UV treatment will enable the company to save 7–35 m3 water and 0.5–2.5 Tm salt per day. In addition to the production process, the advantages on the wastewater treatment must also be considered. Thus, the reuse of the more colored effluents facilitates the treatment of the wastewater generated in other processes. Moreover, the conductivity of the discharged wastewater is reduced as a consequence of salt reuse. All this implies a reduction of discharge taxes and a better accomplishment of regulations.

    As a result of the promising achievements obtained in this study, an industrial system combining electrochemical and UV treatment was designed to treat 4 m3/h in a textile mill in order to evaluate the industrial implementation of the technology.


    4. Conclusions

    Textile effluents collected from industrial reactive exhausted dyebaths were treated by means of an electrochemical treatment at 10 A. In all cases, the treatment provided 100% color removal.

    The residual oxidants were removed by means of UV irradiation. To reduce this step, the optimization of the electrochemical treatment was carried out and it was found that when the treatment is performed at 2 A, 93% color removal is obtained and the concentration of residual oxidants is minimized.

    The effluent reuse study showed that 70% of uncolored effluents could be reused in new dyeing processes. Simultaneously, the reuse of 64% of salt was also achieved.

    The results obtained in this study are promising for the textile industry since this sector consumes large amounts of water. The combined electrochemical and UV treatment enables the reuse of water and salt, which represents a significant advantage from both the environmental and economical points of view.


    Acknowledgment

    This project is co-funded by the European Union within the CIP Eco-Innovation initiative of the Competitiveness and Innovation Framework Programme, CIP: ECUVal project (ECO/13/630452). For more information: www.ecuval.eu.


    Conflict of interest

    The authors declare there is no conflict of interest.


    [1] Charles JM (2013) The Feasibility of Using Raw Liquids from Fast Pyrolysis of Woody Biomass as Fuels for Compression-Ignition Engines: A Literature Review. SAE Int J Fuels Lubr 6: 251-262. doi: 10.4271/2013-01-1691
    [2] Solantausta Y, Nylund NO, Westerholm M, et al. (1993) Wood-Pyrolysis Oil as Fuel in a Direct-Power Plant. Bioresour Technol 46:177-188. doi: 10.1016/0960-8524(93)90071-I
    [3] Chaiaramonti D, Bonini A, Fratini E, et al. (2003) Development of Emulsions from Biomass Pyrolysis Liquid and Diesel and Their Use in Engines―-Part2: Test in Diesel Engines. Biomass Bio energ 25:101-111. doi: 10.1016/S0961-9534(02)00184-8
    [4] Devan PK, Mahalakshii NV (2008) An Experimental Investigation on Performance and Emission Characteristics of Eucalyptus Oil-Diesel Blends in a D.I. Diesel Engine. SAE Paper 2008-01-0757.
    [5] Herchel CM, Seiichi S, Yutaka M (2001) Operation and Combustion Characteristics of a DI Diesel Engine Fueled with Biomass Oil-Diesel Fuel Blends. SAE Paper 2001-28-0030.
    [6] Carlos MM, Morris S (2011) Production of a refined biooil derived by fast pyrolysis of chicken manure with chemical and physical characteristics close to those of fossil fuels. J Env Sci Hea Part B 46: 630-637. doi: 10.1080/03601234.2011.594377
    [7] Augustinova J, Cvengrosova Z, Mikulec J, et al. (2013) Upgrading of biooil from fast pyrolysis. 46th International Conference on Petroleum Processing, June 7, Bratislava, Slovak Republic.
    [8] Xu YF, Hu XG, Li WD, et al. (2011) Preparation and Characterization of Bio-oil from Biomass, In: Dr. Shahid Shaukat Editor, Progress in Biomass and Bioenergy Production, In Tech. Available from: http://www.intechopen.com/books/progress-in-biomass-and-bioenergy-production/preparation-and-characterization-of-bio-oil-from-biomass
    [9] Schnizer MI, Monreal CM, Facey GA, et al. (2007) The Conversion of Chicken Manure to Biooil by Fast Pyrolysis I. Analysis of Biooils by FTIR and NMR Spectroscopy. J Env Sci Hea Part B 42: 71-77.
    [10] Shigeharu K, Takeyuki K (1995) Development of a Rapid Compression-Expansion Machine Simulating Diesel Combustion. SAE Paper 952514.
    [11] Hidenori K, Kentaro N, Tetsuya A (2007) A Study of Effect of Heterogeneity of Oxygen Concentration of Mixture in a Combustion Chamber on Combustion and Emissions of Diesel Engine. SAE Tech Paper 2007-01-1845.
    [12] Heywood JB (1988) Internal Combustion Engine Fundamental. McGraw-Hill, NY: 505-506.
    [13] Jurgen K, Gerhard K, Axel M, et al. (2008) Comparison of exhaust emissions and their mutagenicity from the combustion of biodiesel, vegetable oil, gas-to-liquid and petrodiesel fuels. Fuel 88: 1064-1069.
    [14] Andreas J, Martin M, Stefan P, et al. (2009) Tailor-Made Fuels: The Potential of Oxygen Content in Fuels for Advanced Diesel Combustion Systems. SAE Tech Paper 2009-01-2765.
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