Desorption isotherms and isosteric heat of anaerobic fermentation residues

Department of Building Services and Process Engineering,Faculty of Mechanical Engineering,Budapest University of Technology and Economics,Bertalan Lajos u.4-6,H-1111 Budapest,Hungary

Keywords:Desorption Equilibrium Model Measurement Isosteric heat

ABSTRACT This paper presents the equilibrium desorption isotherms and the isosteric heat of sorption of a mixture containing mechanically dewatered fermentation residue(obtained from a blend of chicken,swine and cattle manure)used in biogas plants and corn spoiled silage in a ratio of 2:1.The moisture desorption isotherms of the fermentation residue were determined at 32°C,40°C and 80°C and in the relative humidity range of 0.057/1 using static gravimetric method.Mathematical equations were used to analyze the desorption data of Modified Henderson,Modified Halsey,Modified Oswin,Modified Chung-Pfost and Modified GAB models.The constants of the model equations were calculated by non-linear regression analysis.The Modified Henderson model fitted to the desorption isotherm data well.Using the proposed function,the final moisture content of the material can be determined as long as it can be dried in infniite time with the drying gas in the given conditions.The isosteric heat of desorption was calculated by using the Modified Henderson model in the studied temperature range based on the Clausius-Clapeyron equation.The isosteric heat varied between 46 kJ·mol-1 and 67 kJ·mol-1 at moisture levelsfor the material.

1.Introduction

The fermentation residue manure obtained during the biogas development can be further used for briquetting,combustion or soil fertility capability replenishment.However,according to the technological specifications,the material has to be dried up to the specified moisture content.Scaling up a drying process and the storage of the material requires the relationship between the equilibrium moisture content and the equilibrium relative humidity of the material to determine the air conditions(temperature,relative humidity)to provide the required final moisture content[1].Mathematical equations are used for modeling the drying and re-wetting properties of the material[2].

Prediction of moisture sorption is based on fitting various models to the experimental moisture sorption data.Three basic techniques of determining adsorption and desorption isotherms have been used.These techniques are the manometric,the gravimetric and the special methods.The static gravimetric experimental technique involves the use of various mixtures of distillated water and sulfuric acid,or other saturated salt solutions[3].This method is recommended as the standard method to determine the sorption isotherms to maintain relative humidity at a constant temperature in enclosed saturated gas[4].Numerous sorption isotherm equations have been developed to model the equilibrium moisture content versus equilibrium relative humidity of different types of biological materials at different temperatures[5],but none of them has the ability to describe this relation with sufficient accuracy.Therefore it is necessary to determine for every special material the most appropriate sorption isotherm mathematical equation[6].The sorption isotherm of various materials has been widely studied and different models and equations have been introduced in the literature.In this paper some articles that deal with the modeling of sorption isotherm with a wide range of relative humidity and temperature were collected to show the variability of the examined materials and the models.The articles dealing with the determination of moisture sorption isotherm were classified by three categories in this study.Firstly,each article,where the adsorption isotherms of material were presented,then articles,where only the desorption isotherms were shown and finally,there is a literature review of articles,where both adsorption and desorption isotherms were investigated.

The adsorption isotherms for four different densities of expanded polystyrene thermal insulation materials were investigated[7].In their research,the logarithm of the equilibrium moisture content at the given relative humidity versus the logarithm of mass densities shows linear trend.The adsorption curves of foamed concrete,mineral wood,extruded and expanded polystyrene,and the results were compared to a standard[8]in[9].Based on experiments the adsorption isotherm of aerogel blankets at different temperatures was created[10].The re-wetting characteristics of additional materials used in the building industry were also investigated[11]for aerated concrete.Moisture adsorption characteristics of various foodstuffs have been reviewed and reported by numerous authors.The moisture adsorption isotherms of a dried sausage were analyzed[12]using sorption isotherm equations of Halsey[13],Oswin[14],Caurie[15],Peleg[16],Smith[17],Henderson[18],Modified-BET[19],Guggenheim-Anderson-De Boer(GAB)[5],Ferro-Fontan[20]and Harkins-Jura[21].The Peleg model was considered the best in predicting the experimental data and the thermodynamic properties.Determining the drying and re-wetting properties of different types of sausage is important for describing the drying process[22].Adsorption isotherms of barley(Hordium vulgare)were determined[23]using Modified Halsey[24],Modified Chung-Pfost[25],Modified Henderson[26]and Modified Oswin[27]models.The models were compared using standard error estimate(SEE),residual sum of squares(SSR)and residual plots.Based on the comparison the Modified Chung-Pfost equation gave the best fit for modeling the adsorption isotherms of barley.Adsorption isotherms of sandesh,which is a milk product of India,were investigated[28].The Caurie's[29]model showed better fit to their experimental results for the adsorption isotherm of sandesh than other examined models.During a comparison of the original and the modified BET,Henderson,Halsey,GAB,and Oswin models describing the adsorption isotherms of chitosan films[30],the modified adsorption models of GAB[31]showed the best fit to their experimental data.

The desorption isotherm defines the moisture content of the material which can be dried by a given air temperature and relative humidity.The equilibrium moisture content is defined with the following expression:

which is the final moisture content of the material(t→∞)[1].The final moisture content is influenced by the properties of the material and the drying gas.Hassini et al.[32]determined the desorption model of prickly pear seeds(Opuntia ficus indica)by using GAB,Oswin,Dent[33],Henderson,and Halsey models.The GAB model was found to be the best in predicting the sorption isotherms.The desorption isotherms and the drying curves of red alga Gracilaria were determined using Halsey,Caurie,BET[34],and Oswin models[35].By the experiments,the Halsey equation was found suitable for predicting the desorption isotherms.

In the literature both moisture adsorption,desorption isotherms and thermodynamical characteristics mainly for agricultural materials and foodstuffs in different Xeand φehave been investigated.The sorption model of a kind of sorghum was studied using Modified Henderson,Modified Halsey,Modified Oswin and Chung-Pfost models[36].The Modified Henderson model offered the best fitting to this material.This material was investigated by other authors as well[37].The Modified Chung-Pfost,the Modified Oswin,the Modified Henderson,the Modified Halsey and the Modified GAB models were fitted to the experimental data of sorghum malt.Differently from Bonner and Kenney[36],the Modified Chung-Pfost model showed the best fit to determine the desorption equilibrium moisture content,while the Modified Oswin model was found suitable for predicting the adsorption equilibrium moisture content.The sorption isotherms of grain and kernel of barnyard millet were investigated[38].The Modified Chung-Pfost model for adsorption and the Modified Oswin model for desorption for this grain were found suitable for predicting φe=f(Xe)relationship.For the kernel the Modified Henderson model was found more appropriate both for the adsorption and desorption isotherms.The adsorption and desorption isotherms of two variates of millet(EX-BORNO;SOSAT C88),using the Modified Halsey,Modified Henderson,Modified Chung-Pfost,Modified Oswin model and Modified GAB models were investigated[39].Differently from Singh et al.[38],the Modified Oswin model was considered the best in predicting the experimental data.During the statistical analysis,the results,which used the Chung-Pfost model,were ignored.The adsorption and desorption isotherms of red alga Gelidium sesquipedale(Rhodophyta)were examined[40]to study the drying process of this material.Third degree polynomial regression of the experimental data for the net isosteric heat depending on the equilibrium moisture content was assumed for both cases.Differently from Lemus et al.[35]they fitted a custom equation.The moisture isotherm data of fourteen Chinese wheat varieties(Tricticum aestivum)were determined using eight sorption models and the Modified Chung-Pfost model was considered the best in predicting the experimental data[41].Their study proved that the wheat grains from different types have similar hygroscopic and thermodynamical properties.The adsorption and desorption isotherms for lal peda,which is a milk product of India,were determined[42].The GAB model was suggested from Halsey,Caurie,Oswin,GAB and Modified Mizrahi[43]models.It was determined that the moisture sorption of the experimental material increased steeply at equilibrium relative humidity above the value of 0.6.Also the Halsey,Caurie,Oswin,GAB and Modified Mizrahi models were used to fit for dietetic Rabri,which is also a milk product of India,at three different temperatures[44].Halsey model for 10°C,Caurie model for 25°C and Modified Mizrahi model for 37°C were fitted.The BET,GAB,Oswin,Halsey,Smith,Iglesias-Chirife[45],and Kühn[46]were used to examine the absorption and desorption isotherms of cassava(Manihot esculenta)[47].In this study the main thermodynamic functions were characterized by power law.The results showed that the GAB model was found suitable for predicting the sorption isotherms of this material.The adsorption and desorption isotherms of a kind of mint leaves and stems were determined using only the GAB model[48].For Hemerocallis fulva and Cymbopogon the adsorption and desorption isotherms using the Oswin,BET,Smith,Halsey,Henderson,and White&Eiring[49]models were determined.The experimental data gave the best fit with the Oswin and White&Eiring models.

The goal of our study was to determine the desorption moisture isotherms and the isosteric heat of a mixture containing mechanically dewatered fermentation residue(obtained from a blend of chicken,swine and cattle manure)used in biogas plants and corn spoiled silage in a ratio of 2:1.At the temperatures of 32°C,40°C and 80°C,the suitability of five commonly used three-parameter moisture isotherm model equations was evaluated.During our work five model equations were investigated,namely the Modified Chung-Pfost,the Modified Henderson,the Modified Oswin,the Modified Halsey and the Modified GAB models.The temperatures characterizing a typical drying process:32-40 °C are the typical temperature values for the constant drying rate period and 80°C can be considered as the final limit temperature of material.

2.Materials and Methods

In order to carry out experiments,a self-developed laboratory experimental apparatus was used,which is suitable to determine the sorption isotherms of the fermentation residue of manure mixture at different temperatures.

2.1.Material

The material in our research was a mixture-contained mechanically dewatered fermentation residue(obtained from a blend of chicken,swine and cattle manure)used in biogas plants and corn-spoiled silage in a ratio of 2:1.A picture of the material is shown in Fig.1.

The dry mass of the material was determined by drying the samples at 105 °C for 24 h in a drying oven.The mass of the material was measured before and immediately after drying using a scale(Sartorius LA 1200S,accuracy of±0.001 g).The moisture content on dry basis can be calculated from the masses:

The tests were performed at 32 °C,40 °C and 80 °C.The initial moisture content of the material at three temperatures were

Fig.1.The experimented fermentation residue mixture.

2.2.Experimental procedure

During the experiments,it was necessary to keep the material at a constant temperature by using a water bath.A thermostat vessel was used for equipment(Grant GLS Aqua 12 Plus,accuracy of±0.1°C,measuring range of ambient～99°C).Fig.2 shows the model of the device.The experimental device consists of seven jars placed into the water bath.Each one had a tight fitting lid and contained various mixture of distillated water and sulfuric acid solution.The samples were placed into a sample holder inside the jars.A suitable solution of the distillated water and sulfuric acid was used to control the partial vapor pressure inside the jars.The jars were filled with the solution so that it did not contact with the material contained in the sample holder.In order to prevent the sample holders from capsizing,a ballast was placed in the bottom of each sample holder.The device was filled with water to completely cover the sealed jars to avoid any moisture condensation inside the jars.

Fig.2.Experimental device for determining the sorption isotherms:(1)thermometer,(2)thermal control,(3)glass jars,(4)sample holder,(5)sample of material,(6)sulfuric acid solution,(7)tight-fitting,(8)ballast,(9)polycarbonate lid,(10)thermostat vessel.

Different concentrations of sulfuric acid were created in the jars.The concentrations of the solutions can be calculated using the mass of the distillated water and sulfuric acid[50]:

where xH2Sis the mass of the sulfuric acid.The concentration was generally 96%.The hygroscopic equilibrium of the material was reached in 3 days.

2.3.Data analysis and modeling

Different temperatures and various concentrations have different vapor pressures.The partial vapor pressure over the solution depends on the concentration of the sulfuric acid solution and on the temperature of the near ambient.The experiments were performed at three different temperatures.The values of the saturated vapor pressures of water were for the three temperatures:pv,sat,32°C=4763 Pa,pv,sat,40°C=7381 Pa and pv,sat,80°C=47370 Pa[50].The effect of the variation in the sulfuric acid concentration at different temperatures to the partial vapor pressure was determined according to Eqs.(4)-(6)[50].

Determination of the partial vapor pressure at 32°C depending on the sulfuric acid concentration:

Determination of the partial vapor pressure at 40°C depending on the sulfuric acid concentration:

Determination of the partial vapor pressure at 80°C depending on the sulfuric acid concentration:

The relative humidity can be calculated as the ratio of the partial and saturation vapor pressures:

After the equilibrium is reached in the drying oven,the moisture content on a wet basis of the small samples:

To determinate the actual sulfuric acid solution concentration,it is necessary to take into account the initial water content in the material,which partly diffuses into the enclosed gas during the experiments.At the start of the experiments a small sample from the material was placed into the drying oven to determine the initial moisture content on a wet basis:

The actual concentration of the sulfuric acid(c*)in the jar can be determined by taking the initial moisture content into account:

Based on the actual concentration values of the solution,the partial vapor pressure can be calculated based on the actual concentration of the solution replacing c*with c in Eqs.(4)-(6).

2.4.Sorption models

Numerous equations have been defined for the sorption isotherms of various food and agricultural products.The five commonly used equations[37]are summarized in Table 1.The models are the Modified Henderson model[51],Modified Chung-Pfost model[25],Modified Halsey model[24],Modified Oswin model[27],and the Guggenheim-Anderson-de Boer(GAB)model modified by Jayas and Mazza[31].All of these five equations are the modified versions,where the temperature is taken into account[30].

Table 1 Moisture sorption isotherm models fit to the moisture sorption data[37]

The constants of the equations(A,B,C)were estimated by fitting the mathematical model's trend line to the experimental data,using a nonlinear regression analysis.The quality of the fitting of different models was evaluated by calculating the total sum of squares(SST),the standard error of estimate(SEE),the sum of squares of residuals(SSR)and the coefficient of determination(R2)between the experimental(φi)and predicted equilibrium relative humidities ^φi.The coefficient of determination(R2)used to be one of the primary criteria for considering the best equation to fit the experimental data[41].

The total sum of squares:

The standard error of estimate:

The sum of squares of residuals:

The most general definition of the coefficient of determination is between the experimental data sets and the predicted data:

Fig.3 shows the explanation of the statistical variables based on a typical sigmoidal shaped sorption isotherm.The diagram shows the predicted equilibrium relative humidity in the function of equilibrium moisture content,the measured points are marked with‘+’.

Fig.3.Explanation of statistical variables.

2.5.Determination of the isosteric heat of sorption

The isosteric heat of sorption or differential enthalpy is the amount of energy required to change a unit mass of a product from liquid to vapor at a particular temperature and relative humidity[44].The isosteric heat is the net isosteric heat plus latent heat of the pure water vaporization:

The application of this method requires data from at least two experimental temperature values.The net isosteric heat of sorption can be calculated using the Clausius-Clapeyron equation at the highest temperature TwP,h=80°C and lowest temperature TwP,l=32°C:

The latent heat of vaporization as a function of the two temperatures[50]:

where MH2Ois 18 g·mol-1.

The average of Eqs.(22)and(22)should be used in Eq.(20).

3.Results and Discussion

3.1.Experimental results

The experiments determining the desorption isotherms of the material were performed at 32 °C,40 °C and 80 °C.The measured actual values of concentration of the sulfuric acid,the relative humidities and the moisture contents on dry basis were collected in Table 2.

3.2.Fitting of sorption models to experimental desorption data

The sorption isotherm curves were fitted to the experimental desorption data.The constants of the sorption isotherm models presented in Table 1 were estimated using a non-linear regression analysis with MagicPlot Pro® software.Fig.4 shows the five desorptionisotherms fitted to the experimental data.The shape of the curves are Type V of Brunauer classification.

Table 2 Temperature-wise equilibrium moisture content data for desorption of the material

Based on the fitting of curves,the sorption isotherm constants and the SST,SEE,SSR and R2values were summarized in Table 3.

3.3.Desorption isotherm

The functions of the model equations applied to the experimental data show different shapes and different coefficients of determinations.The determination coefficient of all equations was above 0.94 as shown in Table 3,so in technical practice all curves fit well on the experimental data,so any of them can be used to describe the sorption isotherm of the material with different accuracy.Based on the statistical tests the Modified Halsey model is the most acceptable for describing the desorption equilibrium moisture content of the material.But the quantitative error values are not an appropriate criteria for the fitting of non-linear sorption isotherm curves[27].In our research it was found that it is not enough to examine the model equation in a narrow range,so the extreme values should also be considered.Taking this into account,the Modified Henderson model fitted the most appropriate way on the endpoint Xe=0 ➔φe=0.The sorption isotherm function is asymptotic and tends to the saturation φe=1.Although the values of the coefficient of determination of the Modified Henderson model did not gave the best fit to the experimental data out of the tested models,but they exceeded R2=0.9.Fig.5 shows the desorption isotherms from the Modified Henderson model for the three examined temperature values of the material.

Fig.6 shows that the sorption isotherm curves tend to the lower moisture content values when increasing the temperature of material.The curves start from the origin and tend to φe=1.The Modified Henderson model equations based on the experiments with their validity:

where 1.91＜Xe＜4.05,

where 1.13＜Xe＜3.55,

where 0.018＜Xe＜0.14.

Fig.4.Comparison of the desorption isotherms of the material by the five sorption isotherm model(a:32°C,b:40°C,c:80°C).

Based on the sigmoidal-shaped curves from the experiments,it can be concluded that by increasing the temperature of the material,the material having a high moisture content converts to a weakly moisturizing potential material.The equilibrium moisture content increases with the equilibrium relative humidity for a constant temperature.The temperature increases with decreasing equilibrium moisture content for a constant equilibrium moisture content,which is typical of agro-materials.Increasing the temperature the excitation states of molecules increase their distance and decrease attractive forces between them.The material became less hygroscopic at highertemperatures.The water molecules detached from the water-binding sites by increasing the temperature of the material.Consequently,an increase of temperature for constant equilibrium moisture content results to higher values of equilibrium relative humidity and causes an increase of the deterioration rate of material[32].

Table 3 Model parameter and fit criteria for the five temperature-dependent isotherm models of the material

3.4.Isosteric heat of desorption

The evaluation of net isosteric heat of sorption at the average material temperature was performed using Eq.(21)to the desorption data at 32°C and 80°C by using the Modified Henderson model.The average value of the latent heat of vaporization was calculated using Eqs.(22)and(23).The validity of the isosteric heat is 1.91＜Xe＜4.05,which is the examined moisture content range of Eq.(24).Fig.5 represents the variation of the isosteric heat calculated using Eq.(20)with equilibrium moisture content.The figure shows that the isosteric heat decreased rapidly as the equilibrium moisture content of the material increased.Large values of Qstat low moisture content show a stronger interaction between the material and water vapor,so initially,the desorption occurs on the most active sites with high interaction energies.The desorption subsequently occurs on the less active sites including lower interaction energies[28].

4.Conclusions

Fig.5.Isosteric heat of sorption of the material.

The purpose of the present study was to determine the desorption isotherms of a mixture containing mechanically dewatered fermentation residue(obtained from a blend of chicken,swine and cattle manure)used in biogas plants and corn spoiled silage in a ratio of 2:1 and to determine its isosteric heat,based on experimental methods.A non-linear regression software was used to fit five moisture sorption isotherm models(Modified Henderson,Modified Chung-Pfost,Modified Halsey,Modified Oswin and Modified GAB)to the experimental data at 32°C,40°C and 80°C.The sigmoidal-shaped curves were compared using the standard error of estimate,mean relative percentage deviation,total sum of squares,the sum of squares of residuals and the coefficient of determination.The equilibrium moisture content data were in good agreement with the equations.The coefficient of determination R2≥0.94 for all experimental data was considered a good fitting.Based on the tests the Modified Henderson proved the best model for predicting the desorption equilibrium relative humidity at low and high equilibrium moisture content.For a constant equilibrium relative humidity,the temperature increased with decreasing equilibrium moisture content.The sorption isotherms can be used to describe drying and storage behavior.The results can be used to model drying processes and even for the design of an appropriate drying equipment.

During the thermodynamic analyses,the isosteric heat was calculated from the Modified Henderson model based on our experiments using Clausius-Clapeyron equation.Illustrating in a diagram the isosteric heat against the equilibrium moisture content was shown to decrease exponentially as moisture content increased,and was varied between 46 kJ·mol-1and 67 kJ·mol-1at equilibrium moisture levels 1.91-4.05

Fig.6.Plot of the chosen sorption isotherm models.

Nomenclature

A,B,C model parameters

c concentration of sulfuric acid solution,%

c* actual concentration of sulfuric acid solution,%

M molar mass,kg·mol-1

m mass,kg

pvpartial vapor pressure of water,Pa

pv,satsaturated vapor pressure of water,Pa

Qstisosteric heat,J·mol-1

qstnet isosteric heat,J·mol-1

R universal gas constant,8.314 J·mol-1·K-1

R2determination coefficient

T temperature,K(°C)

t time,s

X material moisture content on dry basis,

x material moisture content on wet basis,

ΔH latent heat of vaporization,J·mol-1

φ relative humidity(water activity)

Subscripts

a after drying

b before drying

dP dried material

e equilibrium

H2O distilled water

H2S sulfuric acid

h higher value

i index of summation

in initial

l lower value

n stopping point in summation

w moisture in material

wP wet material

Acknowledgment

Special thanks to Dr.Mária Örvös for her help in this work and to Patrik Balázs Gyuricskó and Gyula Schneider for his help during the experiments.This work was supported by Hungarian Ministry of Human Capacities(NTP-NFTÖ-18-B-0420).The research reported in this paper was supported by the Higher Education Excellence Program of the Ministry of Human Capacities in the frame of Water science&Disaster Prevention research area of Budapest University of Technology and Economics(BME FIKP-VÍZ)and by the Hungarian Scientific Research Fund(NKFIH/PD-116326).