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Digestion anaerobia de residuos de alimentos. Prediccion de la produccion de metano mediante la comparacion de modelos cineticos.

Anaerobic digestion of food waste. Predicting of methane production by comparing kinetic models

1. Introduction

The final disposal of municipal solid waste (MSW) into landfills is the most applied worldwide strategy for its handling (Hoornweg et al., 2013). In Latin America, Europe and United States specifically, the fraction of MSW disposed into landfills represent approximately 73, 53 and 34%, respectively (TWB, 2012), which generates environmental impacts as: greenhouse gases-GHG, leachates, volatile organic compounds-VOC, among others. Additionally it causes environmental conflicts due to other issues such the devaluation of the surrounding land costs (Yang et al., 2014).

In developing countries, food waste (FW) represents over 60% of MSW (TWB, 2012; Oviedo et al., 2015). Currently, sustainable technologies such as composting and Anaerobic Digestion (AD) seek to reduce environmental impacts and human health effects, besides increasing the useful lifetime of landfills (Hartmann & Ahring, 2005) and provide added value to FW.

Previous work on the effect of substrateinoculum (S/I: g[V.sub.sustrato] x g[V.sub.inoculo. sup.-1])) ratio in the Biochemical Methane Potential (BMP) assay has been limited (Raposo et al., 2006). The specific methane production rate increases at S/I of 0.5; but at higher ratios, it was found that this rate begins to decline although steadily. The S/I proposed by Owen et al. (1987) as a standard was approximately 1.0; however Raposo et al. (2006) and Parra et al. (2015) recommend defining the S/I ratio that increases methane production according to the substrate to be treated.

The biochemical and physicochemical processes that occurs in AD of FW are influenced by various factors, reason for which is recommended to study this process experimentally by performing the application of kinetic models (Aldin et al., 2011). Inadequate predicting of methane production can lead to erroneous conclusions as underestimation or overestimation of methane generation, whose impact may reduce the reliability and quality of outcomes to optimize the process and to increase the methane production (Gao et al., 2014).

Modeling is an important tool used to assess aspects of bioprocesses and optimization of biological systems. AD is a complex and non-linear bioprocess, and many different approaches have been used in the last two decades for modeling, identification of parameters and validation, with a great variability of results reported, even under the same operational and environmental conditions (Rivera et al., 2009).

The most used kinetic model in batch test is the first order model, since it lets to set the rate of degradation of the substrate in the AD, specifically the hydrolysis rate; however, this model can not evaluate some aspects of great importance during the startup and operation of batch anaerobic reactors (Angelidaki & Sanders, 2004; Trzcinski & Stuckey, 2012; Hidalgo & Martin, 2014). Therefore, the prediction of the behavior of biomass and its relationship with the AD byproducts, mainly methane production, have caused the need to apply other kinetic models that also evaluate another important features as the duration of the lag phase, which is an important parameter in AD and is associated with the acidogenic and acetogenic stages (Aldin et al., 2011).

Other models that have been applied in batch test are: the Transference Function, Logistic Function and Modified Gompertz. The Transference Function or reaction curve is used mainly for control purposes, which considers that any process might be analyzed as a system receiving inputs and generating outputs; Logistics Function assumes that methane production is proportional to the size of the microbial population and to the digestible substrate (Li et al., 2012) and the Modified Gompertz assumes that the rate of methane production is proportional to the microbial activity, but this proportionality decreases with the solids retention time -SRT , which can be interpreted as a loss of efficiency in the rate of substrate conversion over time (Donoso-Bravo et al., 2010).

Although Modified Gompertz Model is one of the most applied kinetic models in the study of factors that affect AD of FW, it presents several drawbacks that affect the prediction of methane production.

Authors such as Donoso-Bravo et al. (2010) found that this model tends to give slightly higher values without providing a biological explanation (negative lag phase) and Li et al. (2011) argue that this model can be altered when S/I ratio is greater than 0.7. However, the few reported studies evaluating kinetic models of AD of FW, may be due to part of them are based on the assumption that the FW are a readily biodegradable substrate and that any model can easily predict methane production under the influence of various factors at the same time.

This research aims to evaluate both, the incidence of S/I ratio on the AD of FW from a university restaurant, as well as the influence of the prediction of methane production by using different semi empirical models for the BMP assays.

2. Materials and methods

2.1 Substrate an inoculum

The FW raw samples were obtained from a restaurant at Universidad del Valle (Cali, Colombia) during 5 weeks (one sample was taken every week) and the physical categorization (mixture of fibers and minerals, carbohydrates, fruits citrus and semi-citrus and non-citrus fruits) was made according to revealed by Oviedo et al. (2014). The physicochemical characterization (pH (UNT), Moisture (%), Total Alkalinity-TA and Bicarbonate-BA (mgCaC[O.sub.3]x[L.sup.-1]), Volatile Fatty Acids-VFA's (mgx[L.sup.-1]), Total and Filtered Chemical Oxygen Demand-COD (mg[O.sub.2]x[L.sup.-1]), Biological Oxygen Demand-BOD5 (mgx[O.sub.2][L.sup.-1]), Total Solids -TS and Volatile-VS (mg[L.sup.-1])) were performed according to procedures described in Standard Methods (APHA, 2005).

Prior to characterization of FW and the BMP assays, the inert material and slow-degrading material (plastic) were removed as recommended by Mukherjee et al. (2008). Afterwards, a shredding process was implemented with a Waring Commercial blender during one minute at a speed of 15800 rpm (standard speed) as suggested by Sharma et al. (1988).

The inoculum was obtained from a UASB reactor of a municipal wastewater treatment plant (WWTP), which was characterized in terms of pH, TA, BA, VFAs, TS and VS. In addition, specific methanogenic activity-SMA (gCODgVS-1d-1) tests were carried out. The FW samples and inoculum were maintained at a temperature below 4[grados]C throughout periods of less than seven days before starting of tests. The results of the physicochemical characteristics of the substrate and inoculum samples were processed by descriptive statistics analysis.

2.2 BMP assays

The quantification of biogas was performed by using the manometric method using an Oxitop[R] system at 35 oC, which is a pressure-monitoring instrument that consists of a 250 mL reactor with a measurement device that is inserted on the mouth of the reactor with a control that uses an infrared interface for data, transfer (Pabon et al., 2012). The tests were performed in a WTW TS 606-G/2-I incubator with intermittent manual agitation for a period of 21 days (Aquino et al., 2007). Based on the recommendations of Aquino et al. (2007), the working volume of the reactors was 200 mL, a free space of 50 mL was left with the aim of store the biogas produced. The volume of methane at standard conditions-SC (T= 273 K and P= 1 atm) was determined by applying the equations suggested by Gimenez et al. (2012), where the ratio of dissolved methane was considered. The pH was 7.0

The nutrient solution used was the recommended by Angelidaki & Sanders (2004). The S/I ratios evaluated were 0.5, 1, 2 and 4g[V.sub.substrate] x g[V.sub.inoculo. sup.-1]) respectively, maintaining 1.5 gVS[L.sup.-1] as a fixed concentration of the inoculum. The experiments were performed in duplicate (n=2) including a control (distilledwater withinoculum) forthe determination ofendogenous methane production.

2.3 Kinetics models

In order to determine the effect of S/I ratio on the BMP assay, an analysis of variance (ANOVA) and Tukey's test at p<0.05 were applied using the software R (i386 3.0.2).

From the experimental data, parameters such as methane volume in time ([V.sub.CH4 (t)]) for each S/I ratio, the duration of the lag phase (X) (hours), the maximum methane production ([P.sub.max]) (mL) and the maximum rate of methane production ([R.sub.max]) (mLx[h.sup.-1]) were determined by using three kinetic models as displayed in Table 1. For each fitted model, corresponding measures of goodness of fit, coefficient of determination ([R.sup.2]) and the Mean Square Error (MSE) were obtained, then it was used the software Minitab 16 to identified the best fit model that maximizes the coefficient [R.sup.2] and minimizes the MSE.

3. Results and discussion

3.1 Characterization substrate and inoculum

The FW presented the following physical composition: 39% fibers and mineral mix (carrot peels, banana, pumpkin, tomato, cucumber and eggs, among others), 33% carbohydrates (banana peels, potato and so on), 15% citrus fruit and semi-citrus (lemon, orange, tangerine, passion fruit, pineapple, guava, grape, and lime) and 13% non-citrus fruits (mango, banana, watermelon, papaya, and apple). These characteristics are similar to those found by other authors like Oviedo et al. (2014) and Alibardi & Cossu (2015). Table 2 presents the results of the physicochemical characterization of substrate and inoculum.

The obtained values for pH, moisture, TA, BA and VFAs of the FW listed in Table 2 correspond to normal values for acidified wastes and are similar to the findings obtained by other authors, such as Pesta (2007) and Zupancic & Ros (2012). The low pH values are related to the high contents of moisture (due to the high amount of raw food wastes), which favors the production of VFAs and decreasing bicarbonate alkalinity, hence an alkaline solution with enough buffer capacity should be used in order to neutralize the acidity during AD of FW (Abdulkarim & Abdullahi, 2010).

All the organic matter indicators of the FW showed high values due to its physical categorization (Oviedo et al., 2014; Parra et al., 2015). Additionally, the [COD.sub.filtered]/[] ratio (0.30) showed high quantities of particulate material that can affect the stage of hydrolysis of the organic matter (Parra et al., 2015).

Regarding inoculum, it presented typical values of anaerobic sludge from municipal WWTP since pH, TA and BA are indicative of good buffer capacity which favors anaerobic digestion (Torres et al., 2009). The VS/TS ratio indicated a greater presence of active biomass, which can be associated with the UASB reactors that allow greater contact between biomass and substrate, enabling more stable microbial consortia compared to conventional reactors and sludge digesters (Alvarez et al., 2006). The SMA was low and typical of anaerobic reactors that treat municipal wastewater (Quintero, 2011).

3.2 Influence of the substrate ratios on methane production

In the Figure 1 the results of BMP for each S/I ratio evaluated is presented.

According to the results of ANOVA (p< 0.05), there are statistically significant differences among the S/I ratios evaluated, being the best S/I ratios below 1, which is in accordance to the findings reported by Raposo et al. (2006), who stated that when organic load increases in the AD of the FW, inhibitory effects may occur due to accumulation of inhibitory substances such as VFA's. In addition, the optimum range of S/I ratios is similar to that reported by authors as Hidalgo & Martin (2014).

The low values of BMP achieved differ from those found by authors like Elbeshbishy et al. (2012), who found methane yields above 660 mLCH4xgVS-1, due to probably to the source of the inoculum used in their study (municipal WWTP with separated sewer systems), unlike the rpresent study where collection networks are combined sewage which generatedanegative dilutioneffect.

About the kinetic performance, Figure 2 and Table 3 show the methane prediction and the kinetic parameters attained by using kinetic models.

Table 3 presented the best results obtained regarding the fitting procedure (maximizing [R.sup.2] and minimizing MSE) attained with the Logistic Function (LF) model for all S/I ratio evaluated (See Figure 2). The values of lag phase duration were shorter in S/I ratios below 1, since these presented the higher [R.sup.2] and the lower MSE. Despite the fact that the S/I ratio of 4 achieved an [R.sup.2] greater than 0.9 and a lag phase of 17.8 hours, the high MSE value indicates a high variability causing that the prediction of methane as well as biochemical phenomena in the AD of the FW are possibly not reliable and may not be extrapolated to conditions of reactors at pilot and real scale.

Although Transference Function (TF) model obtained an [R.sup.2]> 0.9, the results of certain parameters as lag phase indicated that this model is not appropriate to predict methane production. These results are different from those obtained by Deepanraj et al. (2015) who found that the MG model is suitable for determining the lag phase with respect to LF model for the duration of the process of AD of FW. However, Donoso-Bravo et al. (2010) and Gao et al. (2014) during their investigations with organic wastes found that the best model for predicting methane was the TF when making a comparison to MG.

This phenomenon was also observed by Li et al. (2011) who found that lag phase was basically negligible ([lambda] =0) in all of the cases, which from a biological perspective is invalid, since it would break the assumption that microbial consortia were formed by spontaneous generation and thereby these models would not be suitable to predict methane production.

These results suggest that although the kinetic models tested have benefits in terms of predicting methane production and in turn allow enabling a connection with the behaviour of the biomass, it is necessary to incorporate other type of dynamic models that predicts not only the methane production but also the generation or transformation of other substances or operational variables (removal of COD, ammonia nitrogen, alkalinity, VFA's, amongst other parameters) (Liotta et al., 2015).

Models as the ADM1 can be a reliable option in order to evaluate AD and the formation of other substances during the batch process.

4. Conclusions

The substrate-inoculum (S/I) ratio affects the AD of FW. At an S/I ratio below 1, a better production of methane was presented, which means that S/I ratio affect the modelling process. Therefore is highlighted the importance to apply kinetic models for prediction of methane production during BMP assays.

On this study, the Logistic Function was the model with best fit compared to Modified Gompertz and Transfer Function models, in terms of prediction of methane production and lag phase, which can be affected by factors such as the ratio S/I. Therefore, it is necessary to evaluate other more robust models to understand more clearly the phenomena that occur in the anaerobic digestion.

5. Acknowledgements

The authors are grateful to Universidad del Valle for providing financial support to the research project entitled "Utilization of Organic Fraction of Municipal Solid Waste for Methane Production as a Source of Renewable Energy-CI 2856". The authors also thank to COLCIENCIAS for sponsoring the doctoral research fellow Brayan Alexis Parra-Orobio (Convocatoria 617-2013 Colciencias segundo llamado).

6. References

Abdulkarim, B., & Abdullahi, M. (2010). Effect of buffer (NaHC[O.sub.3]) and waste type in high solid thermophilic anaerobic digestion. International Journal of ChemTech Research 2 (2), 980-984.

Aldin, S., Nakhla, G., & Ray, M. (2011). Modeling the influence of particulate protein size on hydrolysis in anaerobic digestion. Industrial and Engineering Chemistry Research 50 (18), 1084310849.

Alibardi, L., & Cossu, R. (2015). Composition variability of the organic fraction of municipal solid waste and effects on hydrogen and methane production potentials. Waste Management 36, 147-155.

Alvarez, J., Ruiz, I., Gomez, M., Presas, J., & Soto, M. (2006). Start-up alternatives and performance of an UASB pilot plant treating diluted municipal wastewater at low temperature. Bioresource Technology 97 (14), 1640-1649.

Angelidaki, I., & Sanders, W. (2004). Assessment of the anaerobic biodegradability of macropollutants. Reviews in Enviromental Sciencia and BioTechnology 3 (2), 117-129.

APHA (American Public Health Association). (2005). Standard methods for examination of water and wastewater. American Water Works Association and Water Environment Federation. Washington D.C., EE.UU.

Aquino, S.F., Chernicharo, L.C.A., Foresti, E., Florencio d.S.M.d.L., & Monteggia, L.O. (2007). Metodologias para determinacao daa atividade metanogenica especifica (AME) em lodos anaerobios. Eng. Sanit. Ambient. 12 (2), 192-201.

Deepanraj, B., Sivasubramanian, V., & Jayaraj, S. (2015). Kinetic study on the effect of temperature on biogas production using a lab scale batch reactor. Ecotoxicology and Environmental Safety 121, 100-104.

Donoso-Bravo. A., Perez, E., & Fdz, P. (2010). Application of simplified models for anaerobic biodegradability tests. Evaluation of pre-treatment processes. Chemical Engineering Journal 160 (2), 607-614.

Elbeshbishy, E., Nakhla, G., & Hafez, H. (2012). Biochemical methane potential (BMP) of food waste and primary sludge: Influence of inoculum pre-incubation and inoculum source. Bioresource Technology 110, 18-25.

Gao, S., Zhao, M., Ruan, W., & Deng, Y. (2014). Kinetics modeling of anaerobic fermentative pro-duction of methane from kitchen waste solid residual. Advanced Materials Research 864-867, 1253-1257.

Gimenez, J., Marti, N., Ferrer, J., & Seco, A. (2012). Methane Recovery Efficiency in a Submerged Anaerobic Membrane Bioreactor (SANMBR) Treating Sulphate-Rich Urban Wastewater: Evaluation of Methane Losses with the Effluent. Bioresource Technology 118, 67-72.

Hartmann, H., & Ahring, B. (2005). Anaerobic digestion of the organic fraction of municipal solid waste: Influence of co-digestion with manure. Water Research 39 (8), 1543-1552.

Hidalgo, D., & Martin, M. (2014). Effects of inoculum source and co-digestion strategies on anaerobic digestion of residues generated in the treatment of waste vegetable oils. Journal of Environmental Management 142 (1), 17-22.

Hoornweg, D., Bhada-Tata, P., & Kennedy, C. (2013). Environment: Waste production must peak this century. Nature 502 (7473), 615-617.

Li, J., Sun, K., He, J., & Wu, Y. (2011). Application of modified Gompertz model to study on anaerobic digestion of organic fraction of municipal solid waste. Huanjing Kexue/Environmental Science 32 (6), 1843-1850.

Li, L., Kong, X., Yang, F., Li, D., Yuan, Z., & Sun, Y. (2012). Biogas production potential and kinetics of microwave and conventional thermal pretreatment of grass. Applied Biochemistry and Biotechnology 166 (5), 1183-1191.

Liotta, F., Chatellier, P., Esposito, G., Fabbricino, M., Frunzo, L., van Hullebusch, E.D., Lens, P.N., & Pirozzi, F. (2015). Modified Anaerobic Digestion Model No.1 for dry and semi-dry anaerobic digestion of solid organic waste. Environmental technology 36 (5-8), 870-880.

Mukherjee, S., Kumar, S., & Devotta, S. (2008). Influence of nitrogen of anaerobic digestion of municipal solid waste in a laboratory scale. Journal of the IPHE 9 (4), 19-24.

Oviedo, E., Marmolejo, L., & Torres, P. (2014). Evaluation of the adittion of wood ashes to control the pH of substrates in municipal biowaste composting. Ingenieria Investigacion y Tecnologia 15 (3), 469-478.

Oviedo, E., Torres, P., Marmolejo, L., Hoyos, V., Gonzales, A., Barrena, C., Komilis, C., & Sanchez, A. (2015). Stability and maturity of biowaste composts derived by small municipalities: Correlation among physical, chemical and biological indices. Waste Management 44, 63-71.

Owen, W., Stuckey, D., Healy, J., Young, L., & McCarty, P. (1987). Bioassay for Monitoring Biochemical Methane Potential and Anaerobic Toxicity. Water Research 13 (6), 485-492.

Pabon, P., Castanares, G., & van Lier, J. (2012). An OxiTop[R] protocol for screening plant material for its biochemical methane potential (BMP).

Water Science and Technology 66 (7), 1416-1423.

Parra, B., Torres, P., Marmolejo, L., Cardenas, L., Vasquez, C., Torres, W., & Ordonez, J. (2015). Efecto de la relacion sustrato-inoculo sobre el potencial bioquimico de metano de biorresiduos de origen municipal. Ingenieria Investigacion y Tecnologia 16 (4), 515-526.

Pesta, G. (2007). Anaerobic digestion of organic residues and waste. In: Oreopoulou, V. & Rus, W. (publishers), Utilization of By-Products and Treatment of Waste in the Food Industry. Springer (Chapter 4).

Quintero, S. (2011). Estudio de consorcios microbioanos para la produccion de biogas a partir de residuos de fique. Tesis de Mastria, Departamento de Ciencas Basicas, Universidad Industrial de Santander, Bucaramanga, Colombia.

Raposo, F., Banks, C., Siegert, I., Heaven, S., & Borja, R. (2006). Influence of inoculum to substrate ratio on the biochemical methane potential of maize in batch tests. Process Biochemistry 41 (6), 1444-1450.

Rivera, S., Aranda, J., Espinosa, T., Robles, F., & Toledo, U. (2009). El modelo de digestion anaerobica IWA-ADM1: Una revision de su evolucion.

Ingenieria Agricola y Biosistemas 1 (2), 109-117.

Sharma, K., Mishra, I., Sharma, M., & Saini, J. (1988). Effect of particle size on biogas generation from biomass residues. Biomass and Bioenergy 17 (4), 251-263.

Torres, P., Rodriguez, J., Barba, L., Marmolejo, L., & Pizarro, C. (2009). Combined treatment of leachate from sanitary landfill and municipal wastewater by UASB reactors. Water Science and Technology 60 (2), 491-495.

Trzcinski, A., & Stuckey, D. (2012). Determination of the hydrolysis constant in the biochemical methane potential test of municipal solid waste. Environmental Engineering Science 29 (9), 848-854.

TWB (The World Bank). (2012). World production of Municipal Solid Waste (MSW), 2012*-2025. shared/PORTAILS/Secteur_prive_developpement/ PDF/SPD15/SPD15_key_data_uk.pdf

Yang, Z., Zhou, X., & Xu, L. (2014). Eco-efficiency optimization for municipal solid waste management. Journal of Cleaner Production 104, 242-249.

Zupancic, G., & Ros, M. (2012). Determination of chemical oxygen demand in substrates from anaerobic treatment of solid organic waste. Waste andBiomass Valorization 3 (1), 89-98.

Brayan A. Parra-Orobio * ([seccion]), Andres Donoso-Bravo **, Patricia Torres-Lozada *

* Escuela de Ingenieria de Recursos Naturales y del Ambiente, Facultad de Ingenieria, Universidad del Valle. Cali, Colombia.

** EscueladeIngenieria Bioquimica,PontificiaUmversidad CatolicadeValparaiso. Valparaiso,Chile.INRIA-Chile.SantiagodeChile,Chile


(Recibido: Abril 05 de 2016-Aceptado: Julio 23 de 2016)

Caption: Figure 1. BMP for each S/I ratio assessed.

Caption: Figure 2. Methane production predictions for each S/I ratio with each kinetic model evaluated.
Table 1. Kinetic models used.

Model                                    Equation

Transfer                 VCH4(t) = [P.sub.max][1-exp[-[R.sub.max]
Function (TF)              (t-[lambda]])/[P.sub.max]]
Logistic Function (LF)   VCH4(t) = [P.sub.max]/1+exp[[R.sub.max]
                           ([lambda]-t)/[P.sub.max] + 2]
Modified Gompertz (MG)   [V.sub.CH4](t) = [P.sub.max]exp[-exp

Source: Adapted from Donoso-Bravo et al. (2010).

Table 2.PhysicochemicalcharacterizationofFWandinoculum.

Parameter                                      FW*n

pH (UNT)                                 5.1[O.sub.3]0.04
Moisture (%)                             86.7[O.sub.3]3.7
TA(mgCaC[O.sub.3][L.sup.-1])            4212.8[O.sub.3]5.2
BA(mgCaC[O.sub.3][L.sup.-1])                    --
VFA(mg[L.sup.-1])                      24611.4[O.sub.3]12.7
[]mgx[L.sup.-1])         125812.3[O.sub.3]479.1
[COD.sub.filtered] (mgx[L.sup.-1])    38187.1[O.sub.3]140.6
[BOD.sub.5](mgx[L.sup.-1])            113346.6[O.sub.3]495.6
VS(mgx[L.sup.-1])                     93256.7[O.sub.3]147.5
TS(mgx[L.sup.-1])                     110735.7[O.sub.3]242.1
VS/TS                                          0.8
SMA**(gCODgV[S.sup.-1]x[d.sup.-1])              --

Parameter                                 Inoculum *n

pH (UNT)                                7.4[O.sub.3]0.2
Moisture (%)                                   --
TA(mgCaC[O.sub.3][L.sup.-1])          2461.4[O.sub.3]378.2
BA(mgCaC[O.sub.3][L.sup.-1])           1277[O.sub.3]279.9
VFA(mg[L.sup.-1])                      873[O.sub.3]104.1
[]mgx[L.sup.-1])                  --
[COD.sub.filtered] (mgx[L.sup.-1])             --
[BOD.sub.5](mgx[L.sup.-1])                     --
VS(mgx[L.sup.-1])                     36783.8[O.sub.3]2116
TS(mgx[L.sup.-1])                     53964[O.sub.3]1603.7
VS/TS                                         0.7
SMA**(gCODgV[S.sup.-1]x[d.sup.-1])           0.012

* n: number of samples (5); **Solution VFA's: (Acetic: Propionic:
Butyric: 73:23:4 %) .

Table 3. Results of kinetic models applied to each S/I ratio.

M    S/I   [lambda]   [CI.sub.95%]    [P.sub.max]   [CI.sub.95%]
             (h)                         (mL)

TF   0.5     0.0           N.I           17.5           N.I
     1.0     0.0           N.I           21.2           N.I
     2.0     0.0           N.I           24.8           N.I
     4.0     0.0           N.I           49.8           N.I
     0.5    143.9     (130.8;158.6)      15.3        (14.7;16)
LF   1.0     63.8       (54.7;74)        17.6        (17.;18.2)
     2.0      49       (39.3;58.4)       24.9       (24.2;25.7)
     4.0     17.8       (15.4;21)        49.3       (48.5;50.1)
     0.5     0.0           N.I           19.5           N.I
MG   1.0     0.0           N.I           19.8           N.I
     2.0     0.0           N.I           24.4           N.I
     4.0     0.0           N.I           49.6           N.I

M    S/I     [R.sub.max]     [CI.sub.95%]   [R.sup.2]    MSE

TF   0.5         0.1             N.I          0.99       0.3
     1.0         0.1             N.I          0.98       8.2
     2.0         0.3             N.I          0.93       2.3
     4.0         2.0             N.I          0.94       5.2
     0.5         0.1           (0;0.1)        0.97       0.7
LF   1.0         0.1          (0.1;0.2)       0.92       2.1
     2.0         0.1          (0.09;0.1)      0.93       2.4
     4.0         1.5           (1;2.7)        0.92       7.2
     0.5        0.14             N.I          0.41      1019.6
MG   1.0         0.1             N.I          0.17       13.9
     2.0         0.2             N.I          0.41       5.7
     4.0         1.2             N.I          0.93       7.3

M: Model; CI: Confidence interval; N.I: No interval
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Author:Parra-Orobio, Brayan A.; Donoso-Bravo, Andres; Torres-Lozada, Patricia
Publication:Ingenieria y Competividad
Article Type:Ensayo
Date:Jun 1, 2017
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